TIME, SPEED & DISTANCE

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GETTING STARTED

☛ Speed = Distance / Time
Speed is generally expressed in terms of km/hr or m/s

☛ 1 km/hr= 1000m/3600s = 5/18 m/s

Thus, in order to convert km/hr to m/s multiply it by 5/18

Similarly, in order to convert m/s to km/hr, multiply by 18/5

Eg. Let us say, a bus is travelling at 54 km/hr. What will be the speed of bus in m/s?

Multiplying 54 by 5/18, we get, 5/18 x 54 = 15 m/s .The bus is travelling at 15 m/s.

Eg. Let us consider a train plying from Mumbai to Pune at 60 km/hr. The distance between the two cities is 180km. One day, due to signaling problems, average speed of train was 45km/hr. How early or late will the train reach its destination?

Soln.

Since the average speed of the train has decreased, the time taken to reach its destination has to increase. So the train will be obviously late.

Let us find out how late the train is:

Time=Distance/Speed.

Usual time taken=180/60=3hrs

Time taken on that particular day=180/45=4hrs.

It takes the train one 1hr more to reach its destination.

☛ If speed of an object increases by y %, time taken to cover same distance will decrease by  100y/(100+y) %.

EXPLANATION

Let the original speed be S1 and the initial time taken be T1.

Increase in speed = y % of S1

= (S1. Y)/100

New speed, say S2 = S1 + Increase in speed

= S1 + (S1. Y)/100

= S1. (1+ (y/100))

= S1. (100 + y)/100

With increase in speed, the time taken to cover the distance has to decrease.

Since we know, distance in both cases is same,

S1. T1 = S2. T2

S1. T1 = S1. (100 + y)/100 . T2

T2 = 100/(100+y) . T1

Decrease in Time

=  T1 – 100/(100+y) . T1

= y/(100+y) . T1

 

% Decrease in time

= [(y/(100+y) . T1)/ T1] x 100

= 100y / (100+y) 

☛ Similarly, if speed of an object decreases by y %, the time taken will increase by 100y/(100-y) %.

Eg. If a man travels at 30 km/h, he reaches his destination late by 10 min but if he travels at 42 km/h, then he reaches 10 min earlier. Therefore, the distance traveled by him is:

Soln:

Let the distance between two places be x and takes y min to reach his destination.

 Since the distance is same in both conditions, we equate both the cases.

Speed1 x Time1 = Speed2 x Time2

30 x (y+10) = 42 x (y-10)

30y + 300 = 42 y – 420

12 y = 720

Thus, y= 60 minutes

If he travels at 30 kmph he covers the distance in 70 minutes.

Therefore, distance = 30 x (70/60) = 35 kms.

  PROBLEMS ON TRAINS

☛ CASE -I : Train overtaking stationary object 

Consider a train overtaking a man standing on a platform.

The distance train has to cover to fully cross the man is equal to the length of the train.

As the man is stationary, time taken to cross the man completely

= Length of train /Speed of the train

☛CASE – II: Man running in same direction as train

Distance to cross the man completely = Length of the train

Relative Speed of train w.r.t man =Speed of train – speed of man

Time taken to cross the man =

Length of train/ (Speed of train – speed of man)

☛ CASE -III: Man Running opposite to train

 

Distance to cross the man completely = Length of the train

Relative Speed of train w.r.t man =Speed of train + speed of man

Time taken to cross the man =

Length of train/ (Speed of train + speed of man)

☛ CASE IV : Crossing stationary objects like platform/bridge/tunnel

  

Distance to completely cross = K+L

Since the other object is stationary, speed of platform = 0

Time taken for train to cross completely = (Length of train + Length of platform)/Speed of train

 

☛ CASE V: Trains moving in opposite direction

 Distance = Sum of the length of both the trains = L + M

Since, moving in opposite direction,

Speed = u+v

Time taken to cover the distance = (L+M)/(u+v)

☛ CASE-VI: Trains moving in same direction

Distance = L+M

Since, moving in same direction,

Speed = u-v

Time taken to cross each other

= (L+M)/(u-v)

  Boats & Streams/ Aeroplane & Wind

☛ Streams oppose the movement of boats if they flow against the direction in which boat moves

☛ At the same time, if the stream flows in the same direction of the boat, speed of boat increases

☛  Let the speed of boat in still water be u km/hr and speed of stream be v km/hr

☛ The speed of boat in upstream (stream opposite to boat) = u-v km/hr

☛ The speed of boat in downstream (stream same direction as boat) = u+v km/hr

Eg. A boat travels 30 km upstream in 6 hours and returns back in 4 hours. Find the speed of boat in still water and the stream.

Soln:.

Let speed of boat in still water be u km/hr

Let speed of stream be v km/hr

Speed of boat in upstream

= u – v = 30/6

= 5 km/hr

Speed of boat in downstream

= u + v = 30/4

= 7.5 km/hr

Solving, we get

Speed of boat in still water (u)

= 6.25 km/hr

Speed of stream (v) = 1.25 km/hr

Races & Games

☛ These problems involve two or more competing players who outscores the other

Eg. A and B run a 100 m race from a same start point. A has a speed of 10 km/hr whereas B has a speed of 8 km/hr. By what distance will defeat B?

Soln:

As we can see, A is faster than B and both start at same point and time. Hence A will obviously win the race.

To find the distance by which A defeats B, let us understand the following diagram

When A reaches end point, B would be some distance away from the end point. Let the distance be ‘x’.

A runs at a speed of 10 kmph =10 x 5/18

= 50/18 m/s

As we know, time = distance /speed

Time taken by A to complete race = 100/(5/18) = 36 sec

When A reaches the end point, B covers,

36 x 5/18 x 8 km/hr = 80 m

Thus A beats B by 20 m

B will complete the race in 100/(5/18 x 8) =45 sec

Therefore, we can also say that, A defeats B by 9sec

Distance by which A defeated B = Time by which A defeated B x Speed of B (loser)

20 m = 9 sec x 5/18 x 8 km/h

Giving a Start

☛ In the above race, if B had started 20 m ahead of A, both would have reached the end point at the same time.

       

In 36 sec, A would have covered 100 m whereas B would have covered only 80 m.

But thanks to the start, both will reach at the same time.

This is known as ‘giving a start of 20m’

☛ If A had given B a start of say 40 m, B has to cover only 60m to finish the race while A has to cover 100m.

        

B covers 60m in 60/ (5/18)x8

= 27 sec.

When B covers, 60 m in 27 sec, while A will only cover

5/18 x 10 x 27 = 75 m.

In this case, B will beat A by 25 m or 9 sec. [As A will reach end point in 36 sec].

PRACTICE PROBLEMS

3
Created on By venkateshj

Time, Speed & Distance - Concept Refresher

1 / 40

Raam walks 700 m in 4 min. Find his speed in kmph

2 / 40

A  train covers 330 km in 6 hours. In order to cover the same distance in one-third of the time taken, what should the speed of train be in kmph?

3 / 40

If a cyclist travels at 28 km/hr instead of 20 km/hr, he would have cycled 28 km more. The actual distance travelled by him is:

4 / 40

A train can travel 60% faster than a car. Both start from point A at the same time and reach point B 80 kms away from A at the same time. On the way, however, the train lost about 24 minutes while stopping at the stations. The speed of the car is:

5 / 40

A man covered a certain distance at some speed. Had he moved 15 kmph faster, he would have taken 12 minutes less. If he had moved 10 kmph slower, he would have taken 12 minutes more. The distance (in km) is:

6 / 40

A man travelled 319 kms in 14 hours. He travelled in tractor at a speed of 17 kmph for sometime and thereafter in car at a speed of 26 kmph. The distance travelled by car is :

7 / 40

It takes 12 hours for a Raphael to cover a distance of 795 kms, if he travels 270 kms by car and 525 kms by bus. Had he travelled 305 kms by car and the rest by bus he would have taken 5 mins more to reach his destination. The ratio of speed of car to that of bus is:

8 / 40

Paul is travelling by a train and is estimated to reach his destination at 5 PM if train travels at 60 kmph. If the train travels at 36 kmph, he will reach his destination at     7 PM. At what time will he reach his destination if he travels at 48 kmph?

9 / 40

In covering a distance of 35 km, Somu takes 90 minutes more than Ramu. If Somu doubles his speed, then he would take 1 hour less than Ramu. Somu's speed is:

10 / 40

A train travels at only 5/9 th of its actual speed and covers 70 Kms in 2 hour 20 minutes. Find the actual speed of the train

11 / 40

Jaya travels 500 km by bus. She travels the first 250 km at a speed of 40 kmph and next 250 km at a speed of 60 kmph. Find the average speed of Jaya throughout the journey.

12 / 40

The ratio of speed between two buses is 3:5 and the second bus covers 280 km in 8 hours. Find the speed of the first bus.

13 / 40

Somesh completes a journey in 4 hours. The first half of the journey is covered at 28 kmph and the second half of the journey is covered in 36 kmph. Find the total journey in km.

14 / 40

In a journey of 1400 km, the train had to be slowed down due to signalling problems. As a result, the average speed of the train reduced by 20 kmph, which in turn increased the time of journey by 8 hours.The actual duration of journey was supposed to be:

15 / 40

A train has an average speed of 44 kmph. Had there been no stoppage, the speed would have been 55 kmph. Find the stoppage time of the train per hour.

16 / 40

A train 400 metres long is running at a speed of 55 km/hr. If it crosses a tunnel in 54 seconds, then the length of the tunnel (in meters) is:

17 / 40

A train 130 metres long is running with a speed of 65 kmph. In what time will it pass a man who is running at 13 kmph in the direction opposite to that in which the train is going?

18 / 40

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 4 kmph and 6 kmph and passes them completely in 7 and 8 seconds respectively. The length of the train is:

19 / 40

Two trains - one with a length 1.5 times of the other, are running on parallel lines in the same direction at 36 km/hr and 60 km/hr. The faster train passes the slower train in 15 seconds. The lengths of trains are:

20 / 40

Two buses are running at 60 km/hr and 33 km/h in the same direction. The faster bus crosses a girl sitting in the slower bus in 10 sec. Find the length of the slower bus.

21 / 40

A 400 metre long train crosses a platform in 22.5 seconds while it crosses a signal pole in 12 seconds. What is the length of the platform?

22 / 40

A train speeds past a pole in 20 seconds and a platform 200 m long in 35 seconds. Its length is:

23 / 40

A train 230 m long is running at a speed of 58.5 km/hr. In what time will it pass a bridge 160 m long?

24 / 40

A train 135 m long passes a man, running at 6 km/hr in the same direction in which the train is going, in 9 seconds. The speed of the train is:

25 / 40

A train running at the speed of 60 km/hr crosses a pole in 12 seconds. What is the length of the train?

26 / 40

Two trains, each 200 m long, moving in opposite directions, cross each other in 12 seconds. If one is moving thrice as fast the other, then the speed of the faster train is:

27 / 40

Two trains are moving in opposite directions at 60 km/hr and 75 km/hr. Their lengths are 400m and 500m respectively. The time taken by the slower train to cross the faster train in seconds is:

28 / 40

Two goods train each 350 m long, are running in opposite directions on parallel tracks. Their speeds are 50 km/hr and 40 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

29 / 40

Two cities A and B are 180 km apart on a straight line. One bus starts from A at 10 a.m. and travels towards B at 40 kmph. Another bus starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

30 / 40

Two buses, one from Pune to Bengaluru and the other from Bengaluru to Pune, start simultaneously. The buses reach their destinations after 3 hours and 5 hours 20 minutes respectively. The ratio of their speeds is:

31 / 40

A boat travels 60 km downstream in 6 hours and the same distance upstream 15 hours. Find the speed of the boat in still water.

32 / 40

Harsha can row 30 km in 5 hours in still water. If the speed of the stream is 4 kmph, he would travel a round trip( upstream and downstream) in 4 hours 48 minutes.  . Find the distance that he would then travel each way.

33 / 40

Vijay rowed a boat in still water at a speed of 10 kmph. He noticed that he was able to row a distance of 3 km against the stream in 30 minutes. How long would he take to row a distance of 35 kms along the direction of stream?

34 / 40

In a given amount time, a boat can either cover a certain distance upstream or 3 times that distance downstream. If the speed of the current is 6 kmph, find the speed of the boat in still water.

35 / 40

In a 400 m race, A defeats B by 40 m or 8 sec. What is the speed of A ?

36 / 40

A takes 240 steps to reach the bottom from top on an upward moving escalator. On the other hand, B takes 30 steps to reach the top in the same escalator. Find the number of steps in stationary escalator if A takes 4 steps in the same time as B takes 1.

37 / 40

An escalator is moving upwards and Ramesh is reaches the top in 90 steps. Suresh is travelling downwards in the same escalator and takes 180 steps to reach the bottom. Had the escalator been stationary, how many steps would have been visible on it?

38 / 40

Rahul is 1.5 times as fast as Sahil. In a race, Rahul agrees to Sahil a head start of 200 m, yet both of them finish the race at the same time. How much distance did Sahil run?

39 / 40

In a 800 m race, Ram gives Shyam a head start of 300 m. The ratio of their speeds is 5:4. By what distance will the winner beat the loser?

40 / 40

In a 600 m race, A beats B by 300 m. In the same race, B beats C by 200 m. By what margin did A beat C in the race?

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