Question

A train starts from Delhi to Kashmir at 8 a.m with a speed of 60 km/h. Another train starts from Kashmir at 5 p.m the same evening with a speed of 90 km/h towards Delhi. The distance between Delhi and Kashmir is 800 km. How far from Kashmir will the two trains meet and at what time will the two trains meet?

Answer 1

Answer:

Time required to reach Kashmir by train A, So, the required time is 13 hours and 19min.

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Answer 2

Given,

A train starting at Delhi at 8 a.m is moving at speed of 60km/h towards Kashmir.

Another train starting at Kashmir at 5 p.m is moving at a speed of 90km/h towards Delhi.

The distance between Kashmir and Delhi is 800 km.

To Find,

The time at which both the trains cross each other and at what distance from Kashmir.

Solution,

Since the first train starts at 8 a.m in Delhi, the train would have traveled for 9 hr before the second train started from Kashmir.

Thus the first train would have traveled a distance of 540 km, that is $(60)(9) = 540$

Now only 240 km is left, for the first train to reach Kashmir.

Now the second train started moving towards Delhi at a speed of 90 km

Let us say the first train crosses the second train after traveling for $t$ hr and after a distance of $x$ km

Thus $60t = x$

Similarly, the second train would have traveled for the same time, that is $t$hr and traveled a distance of $240-x$ km

Thus $90t = 240-x$

⇒ $90t = 240-60t$

⇒ $90t+60t= 240$

⇒ $150t = 240$

⇒ $t = \frac{240}{150} = \frac{24}{15} = 1.6$ hr

⇒ $x = 60(1.6) = 96$ km

Thus the first train and second train will cross each other after a time of 1.6 hr from 5 p.m and at a distance of 144 km from Kashmir.

Henceforth, the two trains will cross each other at 6:36 p.m and at a distance of 144 km from Kashmir.