Question

on a track of 200km a train travels the first 50km at a uniform spee of 40kmph how fast must the train travel the next 150km so as to maintain the average speed of 60kmph for the whole journey

Answer 1

The speed of train for 50 km = 40 km/h
We know that speed = distance/time
40 km/h = 50/time
time = 50/40 = 5/4 h

Let the speed for next 150 km be x km/h
distance = 150 km
time = distance /speed
        = 150/x h

Total distance = 150 km + 50 km = 200 km
Total time = 5/4 + 150/x = (5x + 600)/4x h

Average speed = total distance/total speed
60 km/h = 200/[(5x + 600)/4x]
60 = 800x/(5x + 600)
300x + 36000 = 800x
800x - 300x = 36000
500x = 36000
x = 36000/500
x = 72 km/h 

The train has to travel with 72 km/h for next 150 km to maintain an average speed of 60 km/h

Hope this helps you.

Answer 2

Let AC is the length of railways track

e.g. AC = 200 km

and AB = 50 km ,

Let speed of train for covered rest 150 km = P km/h

we know,

average speed = total distance /total time

total distance = 200 km

and average speed = 60 km/h

total time = ?

total time = 200/60 hours = 10/3 hours

now,

time taken to cover first 50 km with 40 km/h = 50/40 = 5/4 hours .

so, time taken by train to cover next 150 km with P km/h = total time - time taken by train to cover first 50 km

= 10/3 - 5/4 = 25/12 hours

so, speed of train in next 150 km = 150/(25/12) = 150 × 12/25 = 72 km /h