Question

A train covers half of its journey with a speed of 10m/s and the other half with a speed of 40 m/s. Calculate the average speed of the train during the whole journey.

Answer 1

Answer:

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.