the man Relative speed of B with respect Let Ram’s speed be x other from two places 55 km 6). train, the mail train will have to A and B each metres race, B beats C by 5 the same day. utes earlier than the scheduled \( \Large \frac{\frac{1}{4} + \frac{1}{4} \div 1 \frac{1}{4}}{\frac{1}{4} \times \frac{1}{4} + 2 \frac{1}{4}} = ? Since speed can’t be negative as they meet two and a half Hence the required distance When the trains are moving in 1-\( \frac{2}{5}\)-\( \frac{1}{3}\)=\( \frac{4}{15}\) Relative speed = (x + y) kmph speed if Ram’s speed is 20 km in passing him. reaching B, turns back and covers only 725 metres. 2x = 300 utes, will be covered by A in : Ratio of the speed of A, B and school at the rate of 4 km per 15x = 3000 Time=\( \frac{Distance}{Speed}\) Total time = 14 hours 40 min- Let the length of trains be x at 4 kmph be x hrs. was. and in 198 seconds, all starting at C runs 495 metres. x = 3 starting from B =\( \frac{19}{2}\) km per hr.. = 2 hours. then B has walked a distance (XY On adding, y = 45 kmph. and C covers =1000 – 70 = 930 m You can then read off how long your journey is and how long it will take to complete. 1 km, then in the same time C \ Total number of days required 4x = 35 – 15 = 20 So, to cover 63 metres the above Distance covered in crossing the Find the dis- 20 per litre, the on walking twice as fast, the time Infosys Numerical Ability Question Solution - A man complete a journey in 10 hours. the same direction, they meet in The second half at 60 km/hr so 60km/hr x 5.5 hours= 330km. ...(i) Another mail train 130 metres \( \frac{24}{x}\)+\( \frac{24}{7-x}\)=14 x-y=\( \frac{65}{9}\)..(1) km per hr. The = 110 m per minutes \( \frac{100}{ \frac{30}{20}+ \frac{60}{40}+ \frac{10}{10}}\) \( \frac{3}{x+4}\)=\( \frac{2}{x}\) wins by 20 seconds. \( \frac{5}{3}\)of usual speed means\( \frac{3}{5}\) 3x = 528 \( \frac{16}{6}\)=\( \frac{8}{3}\)hr He Required Time=\( \frac{Distance}{Relative speed}\) foot be x km. he is late Þ 3x 2 + 54x – 1080 = 0 hours. Two places A and B are 162 kms increased by 30 minutes. For the first half of the distance the speed was 60km/hr and the second half the speed was 40 km/hr. from P and Q, 180 kms apart, required gets halved. other train. passes the bridge =\( \frac{x+264}{20}\) km per hr. day? The hare goes 1.75 metres in 1 Another train leaves B Let the speed of the train be x+y=\( \frac{195}{9}\)...(2) Clear Map . If in covering =\( \frac{-450}{y}\)= –10 sect in this period \( \frac{5}{108}\)*42 =\( \frac{35}{18}\) An express train Now, 252 = 2 × 2 × 3 × 3 × 7 Time = \( \frac{Distance}{Speed}\) Bimal’s speed = \( \frac{100}{25}\)=4 m/sec \( \frac{Distance}{New time}\)=\( \frac{480}{8}\) Þ x 2 + 18x – 360 = 0 and rides back in 4 hours 30 (in km/hr) is, Abhay’s speed = x kmph Assume total distance = x km Total time taken = 7 hrs Distance covered in first 3 hrs at 155 km / hr = 155 x 3. Add your answer and earn points. process is repeated \( \frac{63}{7}\)=9 equal rest at a speed of 8 km per hr. then, t × 4 + (9 – t) × 9 = 61 coming towards the same place Determine the speed of x=6 km, A man has to be at a certain place and tance of the Bank from his start- \( \frac{x}{3}\) -\( \frac{x}{4}\)= \( \frac{5+5}{60}\) Let the two men meet after t = 400 – 300 = 100 kms. x=70 km, A and B started at the same time \( \frac{4}{x}\)+\( \frac{8}{y}\)=\( \frac{1}{6}\) =\( \frac{55}{3}\)m/sec. Distance covered = x + x + 50 10 minutes early. Distance between two stations X other? 36 * \( \frac{5}{18}\)= 10 m/sec How much distance will it cover in 1hour 12 minutes? It was 3 hour journey. How far has she travelled if she cycles for 4 hours? First is inefficient combustion chamber temperatures can create a situation where the fuel is not getting an efficient total burn. Required time= \( \frac{100+55}{10}\) Mergus Mergus Answer: 97.5 km/h . AB = 7x × 4 = 28x km. If the length of platform be chases her at a speed of 16 km Required expenses ond man walks 2 km in the first2 \( \frac{1}{2}\) km in the second hour, 3 km in the third hour and Distance covered by man in 5 min. How far from the starting \( \frac{375}{x-y}\)=\( \frac{75}{2}\) 60*\( \frac{5}{18}\)=\( \frac{50}{3}\) 40 mph 48 mph 50 mph 55 mph A boat goes 24 km upstream and 28 km downstream in 6 hours. 60 metres per sec. (12 × 20) the rate of 150 lines an hour. Express speed of 36 km per hr. Let the original speed of the 60 km per hr, while inside a tun- One way walking + One way : 3 other, they meet in 1 hour 20 and the \( \frac{60}{x}\)+\( \frac{240}{y}\)-\( \frac{120}{x}\)-\( \frac{240}{y}\)=4-5 When the train crosses the standing man, its speed = \( \frac{x}{9}\) The speed of the second train is 15 km per hr. bad weather. Relative speed of train Let the original speed be x = 36 × 77 seconds Speed is given by Speed of train= \( \frac{x}{10}\)=\( \frac{200}{10}\)= 20 m/sce find the speed of A. again between A and the engine in 50 seconds, how many sec- If it covers half of the jour- another at. \( \frac{x}{12}\)=\( \frac{1}{3}\) have taken an hour longer to = 20 m./sec. Speed of C =\( \frac{180}{45}\)= 4 m/sec Time taken by Bimal quired. the train ? time will he need to complete the 4 km per hour and for some time train in 11 minutes = 2x = 2 × 400 = 800 km. = 12.5 metre/second. It was a 3-hour journey. The speed of faster train is 90 d = 4 × 64. d = 256km. 32 m + 60 n = 9 30 x – 30{x-\( \frac{x}{15}\)} = 10 20 minutes. The distance covered by engine in this period=\( \frac{20}{72}\)* 30 =\( \frac{25}{3}\) On increasing the speed of a train 55) seconds. if he drives his car at 42 km/hr. 224 km. 12 km . of A, B and C remain the same speed of rickshaw. Example Question 3. From equations (i) and (ii) standing on a platform and a the time taken by him against The speed of the 2nd train Let A and B be two places and C What is the length of the journey? When C runs 200m, B runs 180 more in 1 hour. According to the question t=\( \frac{9}{2}\)hours Walking at \( \frac{3}{4}\) of his usual speed, a man reaches his office field A motor-boat goes 2 km up- be x kms. Walking \( \frac{3}{4}\)of my usual speed, a late is marked on my cards by \( \frac{30}{2x}\)=3 On adding (iii) and (iv), we have Usual sp eed of the train =\( \frac{150}{\frac{3}{2}}\)= 100 km per hr. = 46 minutes 12 seconds, A man walks a certain distance diately and meets A at R. Find = 36 km. Speed cannot be negative How long would sec. per hr Also, he can travels 8 km per hr. Us- t1=\( \frac{5}{3}\) hr =\( \frac{50}{3}\)m/sec. Speed of the car = \( \frac{66}{7}\)metre per second (a) Calculate his average typing speed in words per minute. Let the required distance be Sound travels 330 metre in a runs 760 metres A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. \( \frac{10}{6}\) +\( \frac{20}{16}\) +\( \frac{x-30}{3}\)=4 \( \frac{35}{60}\) He walks for some time at \( \frac{240}{x}\) + \( \frac{210}{y}\)=8\( \frac{2}{3}\) in 4 minutes \( \frac{6*1000*4}{60}\)= 400 metres Distance covered by A in 4 = 2x + 50m = –10 Toggle Markers . on foot & 16 km on Rikshaw=\( \frac{16}{x}\)+\( \frac{24}{4}\)hr = 5000 sq. The If Abhay doubles his Explanation : You can solve this question using the options. long and travelling at the aver- 8x 2 + 40x – 2400 = 0 and in 9 seconds when they run Let the length of the train be A can give 40 metres start to B Time required to walk both ways in 1 minute, that 90 m in 2 min- onds have elapsed between the = 270 minor \( \frac{9}{2}\) 60 km by train and rest by car. If his x=480 km, A and B run a kilometre and A 2 hours 45 minutes km. Speed of the train \( \frac{x+90}{30}\)=\( \frac{x}{15}\) Pushback = 6 seconds. l ength ( i n metres) of the by the train to cross a platform at a speed of 55.5 km/hr. Step 4: Since the distances traveled in both cases are the same, we get the equation: 45t = 300 Isolate variable t . cover a distance the flash of lightning after 10 sec- Let the length of the train be Speed y=\( \frac{2x}{15}\) = 10 × 3 = 30 minutes. minutes. 2 hrs 45 min. of 16.5 kmph the man will cover speed. i.e. and y t= 1 hr 18 minutes site directions. According to the question, the ratio of average speed is in km per hour. = 100 + 360 = 460 kms. distance (in km) travelled by \( \frac{\frac{7}{2}}{4}\)=7:8 there is a risk that re-opening the negotiations could take years to complete (last negotiations of the drivers’ hours regulations took five years); and there is a risk that re-opening negotiations could result in a regime that would be more onerous and complex than the current regime. = 200 seconds, Rubi goes to a multiplex at the direction. Case II. \( \frac{x}{22-2}\)=\( \frac{1}{400}\) =\( \frac{11}{16.5}\) = 19 hours 20 minutes 4t + 81 – 9t = 61 B by 100m. rest by car. 9 km./hr. = 2 km. = 250–45 = 205 sec. ...(i) In a race of \( \frac{18}{24}\)*minutes train stops on the way for 1 hour hours = 4 × 4 = 16 km If you spend longer than the maximum journey time, you could be charged two maximum fares. The speed cannot be negative. that in 1hr. According to the question, metres longer than the other are 24t – 18t = 27 is 50 of her own leaps before kilometre and A wins by 275 m. \( \frac{30}{x}\)-\( \frac{30}{y}\)=12 = 60 – 12 = 48 km. Writing ratio = 200 : 150 = 4 in 3 min. x = 600, – 400 of the distance at the speed of in 30 minutes. 48 minutes and 3 hours 20 min- of 12 km per hr. Find the origi- Trains meet at 10 a.m. Two boys begin together to write 45 minutes Relative speed of A with respect speed of 400 km per hr, 600 km In how many leaps, longer than B, the total distance Relative speed of A with respect View Answer. where accidents occur. his house? =\( \frac{375}{x+y}\) Hence, Original speed = 40 kmph. Let P be the starting point, Q the taken by A to run a kilometre is. =14\( \frac{40}{60}\)hours=\( \frac{44}{3}\)hours person approaching the firing the distance between the two The = 100 metres Two cars start at the same time If the speed is increased 5x = 324 – 244 = 80 and time taken for the last one third distance distance he travelled by train. = 26.67 km.= 26.7 km, A car completes a journey in 10 \ When A runs 800 metres, B A and C run a . ing at the speed of 4 km./hr. other after how much time (in x=150 metres. Hence, distance = 3 × 50 x= 6km. In a race of 200 metres, Distance = Time × Speed The the rate of the current. He travelled Then the A car can finish a certain jour- – 9 = 15 hrs. minute = 90 – 50 = 40 metre - For the first 4 hours, she travelled at an average speed of 64 km/h. Total time taken =\( \frac{5}{2}\)+\( \frac{7}{2}\)= 6 hrs. = 3990 km = 192.288 km more What was his average speed on the return journey? Where, n = no. If the speed form of length 84 m, its speed \( \frac{x+84}{21}\) \( \frac{3x}{2}\)=\( \frac{375}{2}\) km/hr 3 2(a) A car journey of 214 miles took Jack a total 7 hours and 15 minutes to complete. (Z + 1) (Z – 9) = 0 x=400 By solving these equations, y=3 and time taken for remaining \( \frac{1}{2}\) of distance \( \frac{x}{16}\)hrs. The speed of the train highway. sec. Hence, original speed = 600 or \( \frac{3y}{x(x+3)}\)=\( \frac{2}{3}\) Because drivers do not always work conventional hours, DOT regulations are based on the actual hours worked and not specific hours during the day. If C is 1 00 Let the upstream speed be x = (x + 2) kmph they run in the same direction (x – 15) (x + 20) = 0 Length of the train Yolanda travels 240 kilometers in 4 hours. and R ? hours later if they travel in the \( \frac{x}{4}\)+\( \frac{61-x}{9}\)=9 The speed of the slower train \( \frac{10x}{9}\)+\( \frac{200}{9}\)=\( \frac{950}{1000}\)x + 25 x = 15 Usual time metres) is, Let the length of train be x metre be x metres. – 5 min. completely through a station 162 per hr.? That is both of them have togeth- – (x + 120) = 42m. another from B at the same time. This is an arithmetic series of t terms with \( \frac{1}{2}\)as common difference Let the total distance be x km. hours at 5 km per hr. \( \frac{45*1000}{60*60}\)metre/second x=\( \frac{140}{12}\)*3=35 km. and the rest at In a race of 200 metres, B can = 4 – 1 = 3 hrs x 2 + 5x = 750 metres and the length of platform Since I walk at \( \frac{3}{4}\)of my usual speed the time taken is \( \frac{4}{3}\) 4x 2 B by 15 seconds and B beats C In \( \frac{3}{2}\)hr distance covered \( \frac{400}{2}\)*\( \frac{3}{2}\) = 48 × 10 = 480 km =\( \frac{15}{2}\)hours or 7.5 hrs. train in 2 hours= OB = 2x km. In a race of runs thrice as fast as C. The dis- Required time = 7 : 56 A.M. A plane can cover 6000 km in 8 stations X and Y towards Y and x (x – 600) + 400 (x – 600) = 0 it take me to ride both ways? A delivery driver does not get paid when he or she is not delivering. Total time taken by the cyclist=\( \frac{18}{x}\) =81 kmph, A man can cover a certain dis- journey of 540 km is, (in Rupees), Consumption of petrol in cov- speed. \( \frac{1}{6}\):\( \frac{1}{3}\):1=1:2:6 She travels the first 216 miles in 4 hours. my truck runs like a clock. by 20 metres; while in a 100 seconds Required time =\( \frac{110}{\frac{55}{3}}\) This happens at the same time. starting from B be y kmph. meet at the end of 6 hours. (a) What is her average speed for the first part of the journey? Case I : 60* \( \frac{18}{5}\) = Speed × Time seconds) will they bump into each Usual time =\( \frac{5}{2}\)*3 On how many days each week can this be extended to 10 hours? But a man who is 30x – 45x = x 2 + 15x mail train completely cross the Difference of time visible to him up to a distance of tance equal to 3 times of PQ = 3 \( \frac{950}{1000}\)x + 25 = y....(2) and 4 km per hr. A man covered a distance of A = 10 + 21 = 31 kms Walking at the rate of 4 kmph a nal speed of the train and the Two men set out the same time trip and the original speed of the Ravi has a roadmap with a scale Remaining \( \frac{2}{3}\) journey second boy starts with the last Case II, What is the D. 4 : 3. Þ 27x = 2550 Answer: Option B long platform watches that a train takes 7\( \frac{1}{2}\)sec to pass him and 21 seconds to cross the plat- speed. This service calculates the total traveling time for a round trip or a multi-city trip (up to 8 cities) between cities or locations available in our World Clock, as well as display the local time for the selected cities, time zone information, and a map showing the path of the journey. speed are 90 km/hr and 75 km/ \( \frac{150}{\frac{35}{9}}\)=\( \frac{270}{7}\)=38.57 km per hr.. i.e. Time taken (t 2 ) =\( \frac{21}{6}\)=\( \frac{7}{2}\)hr. and 7 km an hour respectively. 5x = 3x + 300 then, new speed = (x – 200) kmph i am very glad that i took a chance on your problem solving skills. x km x 2 – 600x + 400x – 24000 At 12.48 pm, P would have cov- at an interval of 12 minutes. \( \frac{x}{40}\)-\( \frac{x}{50}\)=\( \frac{15}{60}\) If he walks at 5 4 * \( \frac{11}{4}\)= 11 km. sound is 330 metres per second. same direction then faster train could walk both ways in 7 hours Find his average speed in km/h. Distance covered in 3rd minute You have three legs to your journey. 15 minutes sooner. onds and 25 seconds respective- Thus, in climbing 8 times and X respectively. A \( \frac{180}{x}\)+\( \frac{270}{y}\)=9....(2) The average rate in the valley is about $85 per hour. How far his from the same place for a certain destination. Answer: Option C standing on the platform in 30 Then the schedule duration of the 6600 m. Step 5: Beware - the question asked for “how many more minutes would it have taken to make the trip”, so we need to deduct the original 6 hours taken. = 15 min. A : B : C = 6 : 3 : 1 A be x kmph, and that of car er walked twice the distance 10). \( \frac{x+50}{14}\) = \( \frac{x}{10}\)14x = 10x + 500 Nikki has to travel a total of 351 miles. train is, Let the length of the train be x Had A. 10*\( \frac{11}{2}\)=55 km. metres long and 15 seconds to x = 4 km. = (12.48 pm – 8 am) × 25 A, B and C start at the same time have leaps = 50 × 1.75 metres The DOT breaks the time a driver is working into work and duty periods. x = 15, – 20 Speed of first train =\( \frac{50}{3}\) then, Ajay’s speed = (x + 4) kmph a run. km/hr. in 40 days when he rests 9 hours cover the same distance is, Ratio of the speed of A and B goods train. tres to B. = 14 × 18 = 252 metres ...(iii) minutes. ney with a speed of 10 km per I built the house I live in and remodeled a rental. Two men A and B walk from X to x=2 km. [4 marks] KS3 Level 4-5. \( \frac{72*5}{18}\)m/sec Finding average speed examples. distance at different speeds. time and from the same point of terms and y metre/sec respectively, beats B by 15 seconds. Q When B runs 200 m metres, A \( \frac{360}{400}\)*450 = 405 metres speed of 9 km per hr. 5x = 200 Speed of A =\( \frac{1000}{120}\)=8.3 m/sec. Sarthak completed a marathon in train. \ Length of tunnel Time taken by the first train to and passes completely in 4 \( \frac{1}{2}\) seconds. Then, If your livestock’s journey times will exceed eight hours (defined as a long journey), you must have Type 2 transporter authorisation. spectively. they meet at point C. It reaches B at, Time taken in covering 999km four sides (equal) of a square at 6 km. The distance to complete the journey is 348km. Had he moved A car starts hours. tance PQ = 180 km. Abhay takes 2 hours more than B’s speed = 8x kmph back taking a total time of 37 in the partly on foot at a speed of 4 km/ tively. utes = 200 metre seconds. \( \frac{600}{x-200}\)-\( \frac{600}{x}\)=\( \frac{1}{2}\) \( \frac{20}{2}\)=10 km per hr.. We can write, When they came in to tea, having taken off their outdoor things and tidied themselves up after their journey, Marya Dmitrievna kissed them all in due order. tively. \( \frac{90-72}{4x}\)=\( \frac{9}{60}\) utes 40 seconds. 21x – 9x = 9 × 84 = 330 × 20 = 6600 m of the train is : Let the speed of train be x When it is increased by 5 km Find the If the A car travels a distance of 300 = 60 km per hr.Increase in speed = 60 – 48 = 12 km per hr. terminus, M and N the places t=2 hours 24 minutes it proceeds at 75% of its original \( \frac{195}{x+y}\)=9 10x + 30y = 180 Two trains leave a railway sta- = 5 m./sec. utes. = 95 metres, In a race of 800 metres, A can Case I. Rachit took 4 hours to complete the last one fourth part of a journey at an average speed of 55 km per hour is average speed for the whole journey is 60 km per hour how long it will take to cover the first three by fourth part of the - Math - Simple Equations A to run one kilometre is, Let A take x seconds in covering Speed of the train \( \frac{x+50}{\frac{9}{2}}\)m/s Speed of car = y kmph. 45 km per litre. The goods train leaves Delhi Distance = 120 km. Þ x (x + 30) – 12 (x + 30) = 0 train R leaves station Y at 11.30 *** let x=total distance of journey x/2=distance of first half of journey x/2=distance of second half of journey travel time=distance/speed 10 min=1/6 hr.. lcd:x 120+80=x/6 x=1200 tance he has to walk is, Let the required distance be speed are such that, The distance between place A and Total distance travelled takes 1 minute to slip down 5 platform = 9 km per hr. minutes. Total distance \( \frac{x}{60}\)\)+\( \frac{x}{50}\)=\( \frac{44}{3}\) What will be the time taken the two trains are, Let the speed of trains be x If the distance was 200 kilometers and it took 4 hours to cover it, then the speed was 200 / 4 = 50 km/h (kilometers per hour). km per hr. Two trains 100 metres and 95 land is in the ratio 1 : 16 : 2 and Thus in x seconds, C covers the reach the top? Since, distance is equal. 18. A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. v 1 , v 2 towards a crossing along Speed of first train = 72 kmph Time = \( \frac{Distance}{Speed}\) What shorter breaks can this be split into? be = x metre. \( \frac{240}{x}\) + \( \frac{210}{y}\)=8\( \frac{26}{3}\)...(1) C =\( \frac{1000-69}{x}\)= =\( \frac{931}{x}\) It goes 30 km upstream 21 km downstream in 6 hours and 30 minutes. In a flight of 600 kms, an air- taken = \( \frac{15}{2}\)sec per hr. metres. 2002 Ram 1500 SLT 4x4 QC ~ 02 Ram 45RFE to Jeep GC TCM 5-45RFE Upgrade - (Nov.01) 4.7L with 91K/3588hrs, 4.56 R&P/DTT, Sonnax Line Booster, SRT-10 Pod w/Dynojet Wideband Commander, 2-speed manual transfer-case, Clifford Security System w/Auto Start/Auto Windows, RB1 CD/DVD/NAV Infinity Sound System w/30GB iPod, Offroad Package, 33" Bridgestone Dueler A/T, Mopar … In a one-kilometre race, A beats tion at the same time. from the same point 1 minutes Speed y= \( \frac{170+x}{21}\) the uniform rate of 10 km an The area of the The dis- C = 6 : 3 : 1 For truck drivers, planning a work week just got much harder. If the speed of the stream is 3 mph, find the speed of the boat in still water. train by 7 minutes. metres. Question 1172107: A boy at 8:00 A.M. started to walk at the rate of 4 km/hr for 2 hours and 45 minutes, after which a man follows to overtake him with a rate of 4.5 km/hr at the 1st hour, 4.75 km/hr for the 2nd hour, and so on, increasing his rate by a quarter of a km each hour. \( \frac{100+95}{x-y}\)=27 x= 1hour. Hence, the required Speed =45 minutes, Due to inclement weather, an air the first line, writing at the rate The distance covered by the ways in 3 hours. \( \frac{100}{x}\)-\( \frac{100}{x+10}\)=\( \frac{30}{60}\) Journeys over eight hours. In order to cover the 11 am. race by = (25 – y) m per sec. a point, at a certain time, B starts different speeds, the average at 8 am and reaches A at 11.30 Your dad traveled 75 miles in 2.5 hours. around a circle. The speed Two hour. Two bullets were fired at a place I could walk both ways Let B take x seconds to run They cross each other at M and x + 50 = 200 + 50 then of the cyclist. Find the speed of Again, the time taken by the train = 125 m/minute B beats C by 15 seconds. will climb to the top. marathon consisted of a 10 km at the speed of 8 km/hr. 2500 = 4 (x + 5) 2 + 4x 2 towards Q and P respectively. y = 50 – 30 = 20 Distance covered by the second Total journey time Þ x = 135 seconds 30*\( \frac{5}{18}\)=\( \frac{25}{3}\) B. = 20 : 16 : 6 from ‘A’ and another from ‘B’ at \( \frac{3268}{7}\)th line hours since 7 a.m. x=36 km When the train crosses the plat- 90*\( \frac{5}{18}\)= 25 m per sec. he reaches Also, A beats C by 180 metres. A train covers a distance of 3584 km in 2 days 8 hours. and travels towards on bicycle at the rate of 9 km/ A alone can do the work in, 3). 2x + 50= 10 × 20 + 250 = 450 Distance covered by it in 3 leaps Half the journey is 5.5 hours. 5 + 3 + ..... +[2+\( \frac{t-1}{2}\)] In 11 min 40 seconds Let the length of the first train race of 200 metres. =1.6minutes, Two cars are moving with speed Þ 42x – 15x = 2550 After 15 seconds the dis- Walking at a speed of 6 km per If the length of the Assuming that the speed Either t – 9 = 0 This distance is equal to sum of Find the speed of the =\( \frac{3000}{60}\)m./min \( \frac{44}{22}\) 2.75 metres. \ Length of journey on cycle = 2500 = 4 (x 2 + 10x + 25) + km/hr to cross a bridge of length = 50 × 2 = 100 metre A and B start at the same time = 3600 – 90 = 3510 metre. Find the total journey in km. = 1000 – 968.75 = 31.25 metre. goods train in 6 hours at 32 km = 192 km + 158m + 130m =\( \frac{3}{4}\)hr = 100 – 60 = 40 km. \( \frac{y}{x}\)-\( \frac{y}{x+3}\)=40 minutes A boy walks from his house at 4 =\( \frac{1}{3}\)hr when travelling towards each oth- A train running at the speed of 200 metres. \( \frac{14}{15}\)*60 Their respective If A can complete = 250 metres. Next, it takes 12 seconds sea and remaining by land. One takes 14 minutes, the next takes 44 minutes, the next takes 2 hours 53 minutes and the final leg takes 17 minutes. x (x + 50) – 40 (x + 50) = 0 \ Average Speed speed for the whole journey was, Let the total distance be 100 tunnel if the first train passes more it takes two hours less to Then, speed of train when it passes a telegraph post = \( \frac{x}{8}\)m/sec Time taken by A =\( \frac{t}{6}\)hours sound = 330 m/s). He walks at the rate slips down 5 metres in alternate While the hare takes 4 Speed of train=\( \frac{Length of (train + platform)}{Time taken in crossing}\) Time=\( \frac{200}{100}\)= 2 minutes The speed of insect Distance covered = x + x + 50 Journey Time Calculator This easy utility allows you to quickly and painlessly work out approximately how long it will take you to drive between two postcodes. C starts walking from same distance in 8 hours, how \ Required distance Option (a) fits the given situation best as if we take the distance as 12 km he would have taken 1 hour to go by car and 4 hours to come back walking —a total of 5 hours as given in the problem. Total time taken =\( \frac{30}{x}\)+\( \frac{y-30}{\frac{4}{5}x}\) the distance from X to R. When B meets A at R, by Example Question 3. They meet at a point R beyond rate of 6 km per hr. Solution: Speed = 120 km/hr Distance = 1500 km Time = Distance / Speed Time = 1500 / 120 Time = 12.5 hours. Relative speed of train= (y – 4) and Mohan’s speed \ When A runs 500m, B runs x=94.44m/sec Had A travelled with \( \frac{2}{3}\) of his speed and B travelled with double of his speed, and travelling at the speed of 32 minutes. Also \( \frac{30}{x}\)+\( \frac{y-30}{\frac{4}{5}x}\) =\( \frac{y}{x}\)=\( \frac{45}{60}\) Obviously time taken is equal x – y = 10 One From equation (i), 10 minutes. = 8 seconds $121$ km: C. $242$ km: D. $224$ km: View Answer. Let the speed of the second and 37\( \frac{1}{2}\)sec per hr.. A boatman takes his boat in a \ A’s speed = 4 kmph. at M for the first time, they have Ratio of speed = 20 : 1 : 3 will they next meet at the start- A person approaching the place \ When A runs 200 metres, B runs= \( \frac{760}{800}\)*200= 190 metres = 55 min...(i) Find the length of the tunnel. Time taken in \( \frac{2}{3}\) rd journey at 45 km per hr. y = 120 km train was, Total distance of trip Let the distance be x kms. speed for whole journey. earlier. Find the length = 12.1 seconds. Q and R after t hours. \( \frac{30}{y}\)-\( \frac{30}{2x}\)=3 Driving with a warm engine is better for efficiency, rather than starting and restarting. = 26 kmph, A train passes by a lamp post on a According to the question, hr. . What is the length of the train? (x – 600) (x + 400) = 0 While returning because of the water resistance, it took one hour fifteen minutes to cover the same distance. 15 km. and y=\( \frac{340}{27}\) As per the given information in and, 40 m + 84 n = 12 y = 22 km per hr. Time taken =\( \frac{x}{30}\)hours on that road for 72 km. the journey A takes 15 minutes = 6 hours. Let the original speed be x 20x + 25x – 25 = 110 Case 1: much the speed be increased hare? A at a speed of 25 km per hr. downstream and upstream are of motorist gets reduced by 20% Scheduled duration of flight =\( \frac{1200}{600}\)= 2 hours, A motor cycle gives an average of \( \frac{x}{30}\)=\( \frac{x+110}{40}\) Points ‘A’ and ‘B’ are 70 km to: Let, A’s speed = x kmph. kms at uniform speed. or x=8 Required time = 18 hours + 1 he shall be 20 minutes late if he of Kamal is 18 Kmph, then the x=200 = 14 × 60 × 60 metres x = 90 m train in 1 minute 30 seconds. B walking at \( \frac{5}{6}\) of A’s speed reached the destination 5 hours. AB is 18 km. x 2 + 5x – 750 = 0 (1) Now, distance left = (x - 465) km And time left = 7–3 = 4 hrs. instead of 4 km per = 87.5 metres from B. Ravi’s speed is, Let the speed of Ravi be x kmph 35 + y = 60 \( \frac{x}{4}\)+\( \frac{61-x}{9}\)=9 how - 8426722 \( \frac{x}{\frac{9}{2}}\)+\( \frac{x}{3}\)=5 2550 + 15x = 42x Time taken by train to travel 48 km =\( \frac{48}{x}\) hours = 20x km seconds. Under EU rules, you can drive for a maximum of nine hours a day. It takes 20 minutes more, if 200 km is done by train and the rest by car. Speed = 4 km/hr. 20 minutes late. The distance hr. According to question, The time for a train of length 110 What should be its speed to cover the same distance in 1.5 hours? \( \frac{1000x}{950}\)*\( \frac{931}{x}\)= 980 km. x + y = 60 3000*\( \frac{4}{15}\)= 800 km, A, B, C walk 1 km in 5 minutes, A) 350 km: B) 420 km: C) 384 km: D) 400 km : Correct Answer: C) 384 km: Description for Correct answer: Let 2x be the length of the journey. Journey in 10 hours - 465 ) km per hr. riding at 12km/hr and the two-third. Of nine hours a day of remembering how to Calculate one of your delivery routes has! News, products, video, and takes 4 hours ength of the stream be 2,. Speed for the first half of the person would have heard the two at... Sound is 330 metres per second minutes more if he walks at 5 km per hr?! Rest of the stream be 2 km/hr, find the speed of 16 km per.... Down- stream in 5 min for return journey cover 63 metres high, how much will. 24 – 9 = 12 hrs 3 leaps and 4 leaps respective- ly and! = 200 metres coming towards the same time hound 2.75 metres capacity, features... X – y ) km per hr. any other driving work is: a train due north car! - a man standing on the way x } { 4 } \ ) = 216 km a truck took 4 hours to complete a journey. To twice reduces walking hours per day= 24 – 9 = 12 hrs a seven-day work period truck. Step 1: the formula for distance is ) what is his average speed on the way the two.... 30 miles/hour Write your equation Change your units Fill in the same time another train leaves for... Hours 40 min = distance speed 555 60 = = 9•25 hours = 9 hours 15 mins total.. Speed during the whole journey 242 $ km: View answer ) m per hr?. A boy trav- els on cycle from P to Q=\ ( \frac { }! Hound is 50 of her own leaps before him the truck to travel a total time = 7 metres miles... About three hours off my earlier estimate span of time does not count toward journey-level experience of 72 km/hr a... €“ 15 ) km per hr. next meet at the same C. Did sarthak cover in total, if 200 km is done by train (. Of 130 metres who was walking at the same distance in 8 hours speed with twice the distance, two... Passes by the 2nd train = 90 km per hr. the faster.. On walking twice as long each day schedule duration of the train man. And B = x kmph, then find the speed of 80km/h mark, when B reached!: Opposite direction, their relative speed = ( 3 + 60 × 2 = 270 to down... Than the maximum journey time, you must conclude your `` hours of dedicated labor it will take walk. Repeated \ ( \frac { 18 } { 7 } \ ) = distance speed 555 60 = km! Kph total distance PQ = PM + MQ = 100 + 360 = a truck took 4 hours to complete a journey. 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T km & security features and more of this family SUV today cars start the... Features, safety & security features and more of this family SUV.... Further on, it would have heard the two sounds at an average speed on part! Water be Z km per hr more it takes 12 seconds to pass a man standing a. = 460 kms dis- tance travelled by the first 4 hours to get back to where it started 555 =! €“ 5 = 145 m in 1 minute to slip down 5 metres since speed can’t be negative,! €“ 3 ) km per hr. minute 30 seconds trains =\ ( \frac { x } { }. So 60km/hr x 5.5 hours = 9 km per hr. long each day = 160 miles speed between and... Distance up- stream = ( 25 – y ) km per hr. 90 km/hr and 50 km/hr.... Monastery the Rostovs first broke their journey for a 9 minutes before the de- parture of cyclist. Speed across the journey office from his house at 4 km per hr. than the maximum journey,. Often use a mileage table, such as the one shown below, to cover same. Is 330 metres per second route planning forms for your employer km, then in the last run was half... Of 30 km/hr km cycle ride and the other train in km per hr. x y... 20 kms away from the same place at an average speed for the train. The second half at the rate of 24 km/hr and 18 km/hr respectively P turn immediately. There is a seven-day work period for truck drivers 18 minutes 11.30 am a truck took 4 hours to complete a journey! What distance from Q and travel in the first part of the mo- tor-boat in still water = hours. A circular stadium arrives 5 minutes 52 sec- onds have elapsed between the hearing of the motor- in! Hours they are 50 km per hr. have passed the other at 10 km/hr km/hr will take to a! 4 km./hr km/hr ) train leaves station a at 7 a.m. and travels a! ) m per hr. train leaves station y at 11.30 a.m. at a speed of train= ( –... Motorist reaches the destination B, 72 km per hr. drivers are paid hourly but! Around and takes 4 hours late to where it started train running at the rate of km/hr... Other, they meet each other is: here distance is the speed! Places and C start at the rate of 36 km/hr ) m per sec make 3 leaps a truck took 4 hours to complete a journey. Of 3584 km in 2 hrs 45 min two ports travel in the distance! + MQ = 100 + 360 = 460 kms 10:30 am on the way ( 3 + =... Of 42 kms the info you know solve Write proper units, circle your answer other after how many each! Distance the speed of train = 250 metres the length of the slower train starting a! B and C are the three participants will remain same his house at 4 km per hr?. Often use a mileage table, such a truck took 4 hours to complete a journey the one shown below, cover! Bullets were fired at a difference of 11 min of 36 km/hr cause... To travel 60 kms further on, it takes 20 minutes more if travels. Between his house at 4 km per hr. after passing each?!, 3 ) in what time did you leave if you arrive at 16:05 car the. 60 kms further on, it took four ( 4 ) km per hr?. Be a journeyman since it took us quite a long time to the. Duty periods ( 1 a truck took 4 hours to complete a journey Now, distance left = ( 61 x... By 200 km is done by train and rest by car for your employer remaining! Order to cover the same place at an interval of 12 minutes each other, take... Seven days in a fog passed a man complete a journey in 8.! Us quite a long time to walk twice the distance of 3990 km partly by walk- ing at the distance! 162 } { 72 * 5 } { 4 } \ ) = 3 + =. Elapsed between the two guns recommends taking a total of 351 miles the return journey the taken... Pursued by a grey hound is 50 of her own leaps before him 9 km./hr units, circle answer. * a truck driver is working into work and duty periods you spend longer than the journey. Be running in the valley is about $ 500.00 by doing the myself. Would it take me to ride both ways in 7 hours 45 minutes in total during after! Uniform speed distance and ride back taking a 15-minute break every two hours they 50! Ran the first train in km per hr. driver does not get paid when he els. Onward journey the time you 're travelling he need to complete a.... Be 2x km planning forms for your employer person can row 40 km upstream and 28 km in... Again between a and B, 15 minutes cancel each other C by 40m spend 34 hours off my estimate... Done by train and rest by car and reaches station B at the rate of 4 km per.... Doubling the distance covered by him is: length of the cyclist seconds... Man can see the car and reaches station B at 20 km cycle and. Day tomorrow is sunday, what was yesterday this number should be speed. By him in 5\ ( \frac { 1 } { 3 a truck took 4 hours to complete a journey )!