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Two trains, X and Y, while traveling towards each other on different tracks, they enter a tunnel that is as long as the combined length of both trains. Train X is 135 meters long, and train Y is 151 meters long. After 10 seconds, the two trains meet inside the tunnel. If their speeds are in a ratio of 5:6, how much length (in m) of train X is still outside the tunnel when it meets train Y?

Question

Two trains, X and Y, while traveling towards each other on different tracks, they enter a tunnel that is as long as the combined length of both trains. Train X is 135 meters long, and train Y is 151 meters long. After 10 seconds, the two trains meet inside the tunnel. If their speeds are in a ratio of 5:6, how much length (in m) of train X is still outside the tunnel when it meets train Y?

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Solution

To solve this problem, we first need to understand that the combined speed of the two trains is equal to the total length of the tunnel divided by the time it takes for the trains to meet.

The total length of the tunnel is equal to the combined length of the two trains, which is 135m + 151m = 286m.

The combined speed of the two trains is therefore 286m / 10s = 28.6 m/s.

The speeds of the two trains are in the ratio 5:6. Therefore, the speed of train X is (5/11) * 28.6 m/s = 13 m/s, and the speed of train Y is (6/11) * 28.6 m/s = 15.6 m/s.

When the two trains meet, they have been moving for 10 seconds. Therefore, train X has moved 13 m/s * 10s = 130m, and train Y has moved 15.6 m/s * 10s = 156m.

Since train X is 135m long and it has moved 130m, there are 135m - 130m = 5m of train X still outside the tunnel when it meets train Y.

This problem has been solved

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