Time, Speed & Distance Practice problems with shortcut tricks

Example 1: Ram has a run up of 100 m. if the speed at which he runs at 36 km/hr how much time does he take to complete his run up?

Now first convert speed into m/s

So 36 km/hr= 36 x 5/18= 10m/s

Time = 100/10= 10 sec

Example 2: A man cover certain distance at 50 km/hr and returns back to starting point at 60 km/hr then find his average speed?

Time speed & distance

Average speed= 2 x 50 x 60/(50+60)

=54.54 km/hr

Example 3: A boy goes to school at a speed of 3 km/hr and returns to his home at spped of 4 km/hr . If he takes 5 hrs in all then what is distance between his home and school?

Let the distance is x km.


Time taken during first journey= x/3 hr

Time taken during second journey=x/3 hr

Now x/3 +x/2=5 hr


X=6 km

Example 4: If instead of going at my usual speed of 30 km/hr , I go to office at 40 km/hr then I reach office 10 minutes early. What is distance traveled?

The equation is quite simple and written as

d/30 – d/40=10/60


Example 5: If instead of going at my usual speed ,I go to office at ¾ of usual speed then I reach office 10 minutes late. What is usual time to cover the distance travelled?

Let the usual time is t min

Time taken at ¾ of usual speed= 4t/3 min

Now 4t/3-t-=10


Example 6: Shaan sees Uma standing at a distance of 200 m from his position. He increased his speed by 50% and hence takes 20 s now to reach her

  1. If he travels at the original speed how much time he will take?
  2. What was his original speed?
  3. What is his new speed?

1.Travelling at 150% of his original speed ie 3/2 times so he should take 2/3 of his original time i.e 20 So original time=30 sec

2.Original speed= 200/30 m/s=> 24km/hr

3. His new speed is 50% more so 24 x1.5=36km/hr

Example 7: A, B and C starts swimming a pool simultaneously. To complete 10 laps A takes 10 min, B takes 8 min and C takes 6 min. What is ratio of speed?

Since the distance is same i.e 10 laps for all three. Speed is inversely proportional to time. So ratio of speed


Example 8: Ram and shyam decide to meet somewhere between their houses, which is 30 km apart. Ram rides at 4 km/hr and shyam at 6 km/hr simultaneously then at what distance from Shyam’s house they will meet?

Now suppose two meets at a distance o X km from shyam’s house . then time taken  by Ram=


Similarly time taken by Shyam=X/6

Since both starts simultaneously so time taken should be equal / soling for X we get

X=18KM from Shyam’s house

Example 9: A man takes 8 hrs to walk a certain place and ride back. However, he could have gained 2 hrs, if he has covered both ways by riding. How long would he take to walk both ways?

Walking time+ Riding time= 8 hr——(1)

2 x riding time= 8-2= 6hrs——–(2)

2 x walking time= 2×8-6=10 hrs

So both ways walking will take 10 hrs.

Example 10. The distance between two stations, Delhi and Amritsar , is 450 km. A train starts at 4 am and moves towards Amritsar at speed of 60 km/hr. Another train starts from Amritsar and moves towards Delhi at speed of 80 km/hr. How far from Delhi two trains will be meeting?

Suppose the train meet at a distance of x m from Delhi. Let the train from Delhi and Amritsar is A and B respectively.

So Time taken by B to cover (450-x) – Time taken by A to cover X = 40/60

450-x/80- x/60= 40/60



Thus the train meets at a distance of 170 km from Delhi

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