Question

A train covers half of its journey with a speed of 20m/s and other half with a speed of 10m/s.

Calculate the average speed of the train during the whole journey​

Answer 1

Explanation:

Average speed = (total distance)/(total time)

Let total distance = d

The train covers distance d/2 at 10 m/s, so the time taken for this half of the journey is t1 = (d/2)/10

similarly, t2 = (d/2)/15

So the total time is

t1 + t2 = (d/20 + d/30) = (5d/60)

So avg speed = distance/time

= d/(5d/60) = 60/5 = 12 m/s

Note that the average is not the arithmetic mean of the two speeds (12.5 m/s) as you might expect. It’s lower than that, because you spend more time travelling at the lower speed than at the higher one.

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Answer 2

For the complete journey, the “average speed” of the train is 12 m/s  

Solution:

Let the total distance travelled by a train be 2S.

The as per the question the half distance that is “S” is travelled by speed 10 m/s.

Also the second half “S” is covered with a speed of 15 m/s.

So time taken =  

Speed

Total distance = 2S

Total time

Speed  

= 12m/s  

12 m/s is the train’s average speed.