Question

a train cover half of its journey with speed of 20 ms^-1 and the other half with a speed of 30 ms^-1 then what is the average speed of the train during the whole journey ?

Answer 1

let the total distance covered by the train be x.

now, the time taken by the train to cover the first half of the distance (x/2) will be

t = distance/speed = (x/2) / 20 = (x/40) secs

also the time taken by the train to cover the second half of the distance will be

t' = (x/2) / 30 = (x/60) secs

so, total time taken will be

T = t + t' = x/40 + x/60

or

T = 5x/120 = x/24 secs

now, the average speed will be given as

v = total distance travelled / total time taken

or

v = x / (x/24)

thus, the average speed will be

v = 24 m/s