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Time, Speed & Distance

Relative speed, trains, races and average speed.

45 solved questions · 15 easy · 20 medium · 10 hard

Take a 10-question quiz on Time, Speed & Distance, no login

Shortcuts & formulas

  • Speed = Distance / Time; Distance = Speed x Time; Time = Distance / Speed.
  • km/h to m/s: multiply by 5/18. m/s to km/h: multiply by 18/5.
  • Average speed = Total distance / Total time. For equal distances at x and y: 2xy/(x+y).
  • Relative speed: opposite directions add (x + y); same direction subtract (x - y).
  • A train crossing a pole or a man covers its own length; crossing a platform covers train + platform length.
  • For a fixed distance, speed and time are inversely proportional (speed ratio a:b means time ratio b:a).
  • If two bodies meet and then take t1 and t2 to finish their journeys, their speed ratio is sqrt(t2) : sqrt(t1).

Solved examples

Try each one first, then open the answer and the step-by-step solution.

Easy questions

Q1.

A car covers 240 km in 4 hours at a uniform speed. What is its speed?

  1. A60 km/h
  2. B80 km/h
  3. C70 km/h
  4. D45 km/h
Show answer & solution

Answer: A. 60 km/h

Solution

Speed = Distance / Time = 240 / 4 = 60 km/h Answer: 60 km/h

Q2.

A bus travels at 72 km/h for 2.5 hours. How far does it go?

  1. A144 km
  2. B180 km
  3. C216 km
  4. D28.8 km
Show answer & solution

Answer: B. 180 km

Solution

Distance = Speed x Time = 72 x 2.5 = 180 km Answer: 180 km

Q3.

How long will a train take to cover 450 km at a speed of 75 km/h?

  1. A5 hours
  2. B7 hours
  3. C6 hours
  4. D8 hours
Show answer & solution

Answer: C. 6 hours

Solution

Time = Distance / Speed = 450 / 75 = 6 hours Answer: 6 hours

Q4.

Convert 54 km/h into m/s.

  1. A194.4 m/s
  2. B18 m/s
  3. C12 m/s
  4. D15 m/s
Show answer & solution

Answer: D. 15 m/s

Solution

1 km/h = 5/18 m/s 54 x 5/18 = 15 m/s Answer: 15 m/s

Shortcut: Divide by 3.6: 54 / 3.6 = 15.

Q5.

Convert 25 m/s into km/h.

  1. A90 km/h
  2. B6.9 km/h
  3. C75 km/h
  4. D100 km/h
Show answer & solution

Answer: A. 90 km/h

Solution

1 m/s = 18/5 km/h 25 x 18/5 = 90 km/h Answer: 90 km/h

Shortcut: Multiply by 3.6: 25 x 3.6 = 90.

Q6.

An athlete runs 100 metres in 20 seconds. What is his speed in km/h?

  1. A5 km/h
  2. B18 km/h
  3. C15 km/h
  4. D20 km/h
Show answer & solution

Answer: B. 18 km/h

Solution

Speed = 100 / 20 = 5 m/s In km/h = 5 x 18/5 = 18 km/h Answer: 18 km/h

Q7.

Meena walks at 5 km/h. How long does she take to walk 12.5 km?

  1. A2 hours
  2. B3 hours
  3. C2.5 hours
  4. D6.25 hours
Show answer & solution

Answer: C. 2.5 hours

Solution

Time = 12.5 / 5 = 2.5 hours Answer: 2.5 hours

Q8.

A and B cover the same distance. Their speeds are in the ratio 4 : 5. If A takes 40 minutes, how long does B take?

  1. A50 minutes
  2. B36 minutes
  3. C30 minutes
  4. D32 minutes
Show answer & solution

Answer: D. 32 minutes

Solution

For the same distance, time is inversely proportional to speed. Time ratio A : B = 5 : 4 B's time = 40 x 4/5 = 32 minutes Answer: 32 minutes

Q9.

A 150 m long train running at 54 km/h crosses a pole. How much time does it take?

  1. A10 seconds
  2. B2.8 seconds
  3. C15 seconds
  4. D8 seconds
Show answer & solution

Answer: A. 10 seconds

Solution

Speed = 54 x 5/18 = 15 m/s Time = Length / Speed = 150 / 15 = 10 s Answer: 10 seconds

Q10.

A bus covers 180 km in 3 hours. At the same speed, how far will it go in 5 hours?

  1. A108 km
  2. B300 km
  3. C240 km
  4. D360 km
Show answer & solution

Answer: B. 300 km

Solution

Speed = 180 / 3 = 60 km/h Distance in 5 h = 60 x 5 = 300 km Answer: 300 km

Q11.

A cyclist covers 1 km in 90 seconds. What is his speed in km/h?

  1. A11.1 km/h
  2. B30 km/h
  3. C40 km/h
  4. D45 km/h
Show answer & solution

Answer: C. 40 km/h

Solution

Speed = 1000 m / 90 s = 100/9 m/s In km/h = 100/9 x 18/5 = 40 km/h Answer: 40 km/h

Shortcut: 3600 / 90 = 40, so he covers 40 km in an hour.

Q12.

Two friends start from the same point and walk in opposite directions at 6 km/h and 4 km/h. How far apart are they after 3 hours?

  1. A6 km
  2. B15 km
  3. C24 km
  4. D30 km
Show answer & solution

Answer: D. 30 km

Solution

Opposite directions: relative speed = 6 + 4 = 10 km/h Distance = 10 x 3 = 30 km Answer: 30 km

Q13.

Two cars start from the same point in the same direction at 60 km/h and 45 km/h. How far apart are they after 4 hours?

  1. A60 km
  2. B420 km
  3. C30 km
  4. D15 km
Show answer & solution

Answer: A. 60 km

Solution

Same direction: relative speed = 60 - 45 = 15 km/h Distance = 15 x 4 = 60 km Answer: 60 km

Q14.

A cyclist rides at 15 km/h. How many metres does he cover in 8 minutes?

  1. A120 m
  2. B2000 m
  3. C1500 m
  4. D2500 m
Show answer & solution

Answer: B. 2000 m

Solution

Speed = 15 km/h = 15000 m per 60 min = 250 m/min Distance = 250 x 8 = 2,000 m Answer: 2000 m

Q15.

Asha cycles 3 km in 40 minutes. What is her speed in km/h?

  1. A4.5 km/h
  2. B0.1 km/h
  3. C2 km/h
  4. D6 km/h
Show answer & solution

Answer: A. 4.5 km/h

Solution

Time = 40 min = 2/3 h Speed = 3 / (2/3) = 4.5 km/h Answer: 4.5 km/h

Medium questions

Q16.

A man drives from A to B at 40 km/h and returns along the same route at 60 km/h. What is his average speed for the whole trip?

  1. A50 km/h
  2. B52 km/h
  3. C48 km/h
  4. D24 km/h
Show answer & solution

Answer: C. 48 km/h

Solution

Equal distances, so average speed = 2xy/(x+y) = 2 x 40 x 60 / (40 + 60) = 4800 / 100 = 48 km/h Answer: 48 km/h

Shortcut: Do not take the simple average (50); use 2xy/(x+y).

Q17.

A train goes from Pune to Mumbai at 60 km/h and comes back at 90 km/h. Find its average speed for the round trip.

  1. A75 km/h
  2. B70 km/h
  3. C36 km/h
  4. D72 km/h
Show answer & solution

Answer: D. 72 km/h

Solution

Average speed = 2xy/(x+y) = 2 x 60 x 90 / 150 = 10800 / 150 = 72 km/h Answer: 72 km/h

Q18.

A 200 m long train running at 72 km/h crosses a platform 300 m long. How long does it take?

  1. A25 seconds
  2. B10 seconds
  3. C15 seconds
  4. D6.9 seconds
Show answer & solution

Answer: A. 25 seconds

Solution

Speed = 72 x 5/18 = 20 m/s Distance = 200 + 300 = 500 m Time = 500 / 20 = 25 s Answer: 25 seconds

Q19.

A train running at 90 km/h crosses a pole in 12 seconds. What is the length of the train?

  1. A1080 m
  2. B300 m
  3. C250 m
  4. D200 m
Show answer & solution

Answer: B. 300 m

Solution

Speed = 90 x 5/18 = 25 m/s Length = Speed x Time = 25 x 12 = 300 m Answer: 300 m

Q20.

Two trains of lengths 120 m and 180 m run on parallel tracks in opposite directions at 54 km/h and 36 km/h. How long do they take to cross each other completely?

  1. A60 seconds
  2. B20 seconds
  3. C12 seconds
  4. D10 seconds
Show answer & solution

Answer: C. 12 seconds

Solution

Relative speed = 54 + 36 = 90 km/h = 90 x 5/18 = 25 m/s Total distance = 120 + 180 = 300 m Time = 300 / 25 = 12 s Answer: 12 seconds

Q21.

A train 150 m long running at 72 km/h overtakes another train 100 m long running at 36 km/h in the same direction. How long does it take to pass it completely?

  1. A8.3 seconds
  2. B15 seconds
  3. C10 seconds
  4. D25 seconds
Show answer & solution

Answer: D. 25 seconds

Solution

Relative speed = 72 - 36 = 36 km/h = 10 m/s Distance = 150 + 100 = 250 m Time = 250 / 10 = 25 s Answer: 25 seconds

Q22.

A person travelling at 40 km/h reaches his destination 20 minutes late. Travelling at 50 km/h he would reach 10 minutes early. What is the distance?

  1. A100 km
  2. B80 km
  3. C120 km
  4. D150 km
Show answer & solution

Answer: A. 100 km

Solution

Let distance = d km. Difference in time = 20 + 10 = 30 min = 1/2 h d/40 - d/50 = 1/2 d (5 - 4)/200 = 1/2, so d = 100 km Answer: 100 km

Q23.

Walking at 3/4 of his usual speed, a man reaches his office 20 minutes late. What is his usual time to reach the office?

  1. A20 minutes
  2. B60 minutes
  3. C80 minutes
  4. D26.7 minutes
Show answer & solution

Answer: B. 60 minutes

Solution

At 3/4 speed, time becomes 4/3 of the usual time. Extra time = (4/3 - 1) x usual = (1/3) x usual = 20 min Usual time = 60 minutes Answer: 60 minutes

Q24.

In a 1 km race, A finishes in 4 minutes and B finishes in 5 minutes. By how many metres does A beat B?

  1. A250 m
  2. B100 m
  3. C200 m
  4. D800 m
Show answer & solution

Answer: C. 200 m

Solution

B's speed = 1000/5 = 200 m/min In 4 minutes B covers 200 x 4 = 800 m A wins by 1000 - 800 = 200 m Answer: 200 m

Q25.

In a 100 m race A runs at 8 m/s and B at 6 m/s. What head start should A give B so that both reach the finish line together?

  1. A20 m
  2. B30 m
  3. C40 m
  4. D25 m
Show answer & solution

Answer: D. 25 m

Solution

A's time = 100/8 = 12.5 s In 12.5 s, B runs 6 x 12.5 = 75 m So B must start 100 - 75 = 25 m ahead Answer: 25 m

Q26.

Two towns are 180 km apart. Two cars start at the same time from the towns towards each other at 40 km/h and 50 km/h. After how many hours do they meet?

  1. A2 hours
  2. B18 hours
  3. C4 hours
  4. D4.5 hours
Show answer & solution

Answer: A. 2 hours

Solution

Relative speed = 40 + 50 = 90 km/h Time = 180 / 90 = 2 hours Answer: 2 hours

Q27.

Two stations are 240 km apart. A train leaves station P at 8 am at 40 km/h. Another leaves station Q at 9 am at 60 km/h towards P. At what time do they meet?

  1. A10 am
  2. B11 am
  3. C12 noon
  4. D10:30 am
Show answer & solution

Answer: B. 11 am

Solution

By 9 am the first train has covered 40 km, so 240 - 40 = 200 km remain. Relative speed = 40 + 60 = 100 km/h Time after 9 am = 200 / 100 = 2 h, so they meet at 11 am Answer: 11 am

Q28.

A man walks for 2 hours at 4 km/h and then rides for 3 hours at 20 km/h. What is his average speed for the whole journey?

  1. A12 km/h
  2. B13 km/h
  3. C13.6 km/h
  4. D14.4 km/h
Show answer & solution

Answer: C. 13.6 km/h

Solution

Distance = 2 x 4 + 3 x 20 = 8 + 60 = 68 km Time = 2 + 3 = 5 h Average speed = 68 / 5 = 13.6 km/h Answer: 13.6 km/h

Q29.

A train 300 m long running at 63 km/h crosses a man walking at 3 km/h in the same direction. How long does it take?

  1. A16.4 seconds
  2. B17.1 seconds
  3. C20 seconds
  4. D18 seconds
Show answer & solution

Answer: D. 18 seconds

Solution

Relative speed = 63 - 3 = 60 km/h = 60 x 5/18 = 50/3 m/s Time = 300 / (50/3) = 18 s Answer: 18 seconds

Q30.

A 250 m long train running at 54 km/h crosses a man coming towards it at 6 km/h. How long does the train take to pass him?

  1. A15 seconds
  2. B18.75 seconds
  3. C16.7 seconds
  4. D12 seconds
Show answer & solution

Answer: A. 15 seconds

Solution

Relative speed = 54 + 6 = 60 km/h = 50/3 m/s Time = 250 / (50/3) = 15 s Answer: 15 seconds

Q31.

A cyclist covers the first half of a journey at 20 km/h and the second half at 30 km/h. If the whole journey takes 5 hours, what is the total distance?

  1. A125 km
  2. B120 km
  3. C150 km
  4. D100 km
Show answer & solution

Answer: B. 120 km

Solution

Let total distance = d km. Time = (d/2)/20 + (d/2)/30 = d/40 + d/60 = d/24 d/24 = 5, so d = 120 km Answer: 120 km

Q32.

Two cars travel the same 180 km route at 60 km/h and 45 km/h. How much longer does the slower car take?

  1. A2 hours
  2. B1.5 hours
  3. C1 hour
  4. D4 hours
Show answer & solution

Answer: C. 1 hour

Solution

Time of faster = 180/60 = 3 h Time of slower = 180/45 = 4 h Difference = 1 hour Answer: 1 hour

Q33.

Walking at 5/6 of his usual speed, a boy reaches school 12 minutes late. How many minutes does he usually take?

  1. A72 minutes
  2. B48 minutes
  3. C50 minutes
  4. D60 minutes
Show answer & solution

Answer: D. 60 minutes

Solution

At 5/6 speed, time = 6/5 of the usual time. Extra = (6/5 - 1) x usual = (1/5) x usual = 12 min Usual time = 60 minutes Answer: 60 minutes

Q34.

Excluding stoppages, a bus runs at 54 km/h; including stoppages it runs at 45 km/h. For how many minutes does the bus stop per hour?

  1. A10 minutes
  2. B12 minutes
  3. C9 minutes
  4. D15 minutes
Show answer & solution

Answer: A. 10 minutes

Solution

In 1 hour the bus loses 54 - 45 = 9 km because of stops. Time to cover 9 km at 54 km/h = 9/54 h = 10 min Answer: 10 minutes

Q35.

Ravi goes to his office at 30 km/h and returns along the same road at 20 km/h. If the total time taken is 5 hours, how far is his office?

  1. A125 km
  2. B60 km
  3. C30 km
  4. D120 km
Show answer & solution

Answer: B. 60 km

Solution

Let distance = d km. d/30 + d/20 = 5 (2d + 3d)/60 = 5, so d = 60 km Answer: 60 km

Hard questions

Q36.

Two trains start at the same time from stations X and Y towards each other. After meeting, train A takes 9 hours to reach Y and train B takes 16 hours to reach X. What is the ratio of the speed of A to the speed of B?

  1. A3 : 4
  2. B16 : 9
  3. C4 : 3
  4. D9 : 16
Show answer & solution

Answer: C. 4 : 3

Solution

After meeting, speeds are in the ratio sqrt(time of B) : sqrt(time of A). SA : SB = sqrt(16) : sqrt(9) = 4 : 3 Answer: 4 : 3

Shortcut: Ratio of speeds = square root of the inverse ratio of the post-meeting times.

Q37.

Two runners start together from the same point of a 360 m circular track and run in opposite directions at 4 m/s and 6 m/s. After how many seconds will they first meet again at the starting point?

  1. A36 seconds
  2. B90 seconds
  3. C360 seconds
  4. D180 seconds
Show answer & solution

Answer: D. 180 seconds

Solution

Runner 1 takes 360/4 = 90 s per lap; runner 2 takes 360/6 = 60 s per lap. Both are at the start together when time is a common multiple of 90 and 60. LCM(90, 60) = 180 s Answer: 180 seconds

Q38.

A train passes a man walking at 2 m/s in the same direction in 23 seconds, and passes another man walking at 3 m/s in the opposite direction in 18 seconds. What is the speed of the train in km/h?

  1. A72 km/h
  2. B20 km/h
  3. C60 km/h
  4. D90 km/h
Show answer & solution

Answer: A. 72 km/h

Solution

Let train speed = v m/s and length = L m. L = (v - 2) x 23 and L = (v + 3) x 18 23v - 46 = 18v + 54, so 5v = 100 and v = 20 m/s In km/h = 20 x 18/5 = 72 km/h Answer: 72 km/h

Q39.

A train crosses a 600 m long bridge in 40 seconds and passes a signal post in 15 seconds. What is the length of the train?

  1. A240 m
  2. B360 m
  3. C400 m
  4. D450 m
Show answer & solution

Answer: B. 360 m

Solution

Let train length = L m, speed = v m/s. L = 15v (pole) and L + 600 = 40v (bridge) 15v + 600 = 40v, so v = 24 m/s L = 15 x 24 = 360 m Answer: 360 m

Q40.

Two trains have a combined length of 500 m. Running in opposite directions they cross each other in 10 s; running in the same direction they take 50 s. What is the speed of the faster train in km/h?

  1. A72 km/h
  2. B90 km/h
  3. C108 km/h
  4. D120 km/h
Show answer & solution

Answer: C. 108 km/h

Solution

Sum of speeds = 500/10 = 50 m/s; difference = 500/50 = 10 m/s Faster = (50 + 10)/2 = 30 m/s In km/h = 30 x 18/5 = 108 km/h Answer: 108 km/h

Q41.

A car covers three equal parts of a journey at 20 km/h, 30 km/h and 60 km/h respectively. What is its average speed for the entire journey?

  1. A36.7 km/h
  2. B36 km/h
  3. C40 km/h
  4. D30 km/h
Show answer & solution

Answer: D. 30 km/h

Solution

Let each part = d km. Total distance = 3d. Total time = d/20 + d/30 + d/60 = (3d + 2d + d)/60 = d/10 Average speed = 3d / (d/10) = 30 km/h Answer: 30 km/h

Q42.

A man travels a certain distance at a uniform speed. If he travelled 3 km/h faster he would take 2 hours less, and if he travelled 3 km/h slower he would take 3 hours more. What is the distance?

  1. A180 km
  2. B120 km
  3. C150 km
  4. D210 km
Show answer & solution

Answer: A. 180 km

Solution

Let speed = s, distance = d. d/s - d/(s+3) = 2, so 3d = 2s(s+3) d/(s-3) - d/s = 3, so 3d = 3s(s-3) Equate: 2(s+3) = 3(s-3), so s = 15 km/h d = 2 x 15 x 18 / 3 = 180 km Check: 180/15 = 12 h; 180/18 = 10 h; 180/12 = 15 h Answer: 180 km

Q43.

Train A leaves a station at 48 km/h. One and a half hours later, train B leaves the same station on the same track at 72 km/h. How far from the station will B overtake A?

  1. A144 km
  2. B216 km
  3. C108 km
  4. D288 km
Show answer & solution

Answer: B. 216 km

Solution

Head start of A = 48 x 1.5 = 72 km Relative speed = 72 - 48 = 24 km/h Time for B to catch up = 72 / 24 = 3 h Distance from station = 72 x 3 = 216 km Answer: 216 km

Q44.

In a 100 m race A beats B by 20 m, and in a 100 m race B beats C by 10 m. By how many metres does A beat C in a 100 m race?

  1. A30 m
  2. B25 m
  3. C28 m
  4. D32 m
Show answer & solution

Answer: C. 28 m

Solution

When A runs 100 m, B runs 80 m. When B runs 100 m, C runs 90 m, so when B runs 80 m, C runs 80 x 90/100 = 72 m When A runs 100 m, C runs 72 m A beats C by 100 - 72 = 28 m Answer: 28 m

Shortcut: C runs (80/100) x (90/100) x 100 = 72 m when A finishes.

Q45.

Delhi and Agra are 410 km apart (treat as a straight route). A train leaves Delhi for Agra at 8 am at 50 km/h. Another leaves Agra for Delhi at 9 am at 70 km/h. How far from Delhi do the trains meet?

  1. A150 km
  2. B210 km
  3. C240 km
  4. D200 km
Show answer & solution

Answer: D. 200 km

Solution

By 9 am the first train has covered 50 km, so 410 - 50 = 360 km remain. Relative speed = 50 + 70 = 120 km/h Time to meet after 9 am = 360 / 120 = 3 h First train travels 4 hours in all: 50 x 4 = 200 km from Delhi Answer: 200 km

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