Question

On a 200 km track,a train travelles first 50 km at a uniform speed of 40 km/h. How fast should it travel the next 150 km to maintain an average speed of 60 km/h for the whole journey

Answer 1

First let us find the time taken for the first 50 kms(t1)
t1 = distance/speed
t1 = 50/40
t1 = 5/4 hrs.

now let us find the time taken for the whole journey(T)
T = d/s
T = 200/60
T = 20/6
T = 10/3

now let us find the leftover time(t2)
t2 = T - t1
t2 = 10/3 - 5/4 (LCM is 12)
t2 = (40-15)/12
t2 = 25/12

now with the time and distance let us find the speed.
S = d/t
S = 150/25/12
S = 150 x 12/25( 25 x 6 =150)
S = 6 x 12
S = 72km/hr

checking
average speed = total distance/total time
Avg. Speed = 200/10/3
Avg. speed = 200 x 3/10
Avg. speed = 20 x 3
Avg. speed = 60km/hr.

Answer = 72km/hr