Question

On a 200 km track, a train travels the first 50 km at a uniform speed of 40 km per hour.How fast the train must travel the next 150 km so as to maintain the average speed of 60 km per hour for the whole journey?

Answer 1

The total distance of the track = 200 km

Speed of train for first 50 km = 40 km/h

So, time taken by the train to cover first 50 km = 50/40 = 5/4 h

Let the speed of train for next 150 km in order to maintain an average speed of 60 km/h = x km/h

Therefore, time taken by the train to cover next 150 km = 150/x hours

Average speed = total distance traveled / total time taken.

60 km/h = 200/(5/4 + 150/x)

60 = 200/(5x + 600)/4x

60 = 200*4x/(5x + 600)

300x + 36000 = 800x

500x = 36000

x = 360/5 = 72 km/h.

The train must travel with 72 km/h in order to maintain an average speed of 60 km/h.

Hope this helps you.

Answer 2

average velocity = final + initial/2
60 = x + 40/2
60×2 = x + 40
120 = x + 40
120 - 40 = x
80 = x