Question

A train travels the first 30 km of 120 km track with a uniform speed of 30 km/h.What should be the speed of the train to cover the remaining distance of the track so that it's average speed is 60km/h for the entire trip?

Answer 1

average speed = total distance/total time taken
let remaining distance covered by train with speed x km/h
we know,

time =distance /speed

total time taken = 120/60 = 2 hour
first 30 km time taken by train = 1 hour
and 2nd 90km train taken time = 2-1 = 1 hour
speed of train covered remaining speed = remaining distance/time taken
=90/1 = 90km/h

Answer 2

                           ANSWER                            

                          In the first 30 km speed of the train, v1 = 30 km/h

                          Speed of the train in the next 90 km, v2 (to be determined)

                         Average speed = 60 km/h = (v1 + v2)/2  

                                         = (30 km/h + v2)/2  

                              → v2 = 90 km/h