Question

On a 100 km track, a train travels the first 30 km at a uniform speed of 30 km/h. How fast me
the train travel the next 70 km, so that the average speed of train for the entire trip becom
40 km/h ?


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Answer 1

Given :

Distance 1 = 30 km

Distance 2 = 70 km

We know that speed = distance/time

and,

Average speed = total distance/total time taken

When the train acquired a speed of 30 km/hr, the time taken = 30/30 = 1 hour

Average speed = (distance 1 + distance 2)/(time 1 + time 2)

AS time 2 or t2 is time taken for the second part of the journey of 70 km

⇒ 40 = 100/(1 + t2)

⇒ 40 + 40t2 = 100

⇒ 40t2 = 100 - 40

⇒ 40t2 = 60

⇒ t2 = 60/40

t2 = 1.5

So, t2 or time taken to travel the second part of the journey is 1.5 hours.

Speed of the second part of the journey = distance 2/time 2

⇒ 70/1.5

⇒ 46.666 km/hr or 46.7 km/hr.

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Answer 2

Explanation:

The time taken to travel 30 km (D1) is 30 km/hr. The average speed to travel the whole 100 km is average 40km/hr