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An express train travel from A to B for 4 hours. A normal train travel from B to A for 10 hours. Both of them started at the same time. The average speed of the express train is greater than the average speed of the normal train 90km/h. Find the average speed of the normal train?

1 Answer

1 vote

Answer:

The speed of the normal train is 60 kilometers per hour.

Explanation:

Let suppose that both trains move at constant speed and cover the same distance. Then, we have the following identity:


v_(1)\cdot t_(1) = v_(2)\cdot t_(2) (1)

Where:


v_(1), v_(2) - Average speeds of the express train and the normal train, in kilometers per hour.


t_(1), t_(2) - Travel times of the express train and the normal train, in hours.

In addition, there is the following relationship between average speeds:


v_(1) = v_(2) + 90 (2)

By (2) in (1), we have the following expression for the average speed of the normal train:


(v_(2) + 90) \cdot t_(1) = v_(2)\cdot t_(2)


90\cdot t_(1) = v_(2) \cdot (t_(2) - t_(1))


v_(2) = (90\cdot t_(1))/(t_(2)-t_(1))

If we know that
t_(1) = 4\,h and
t_(2) = 10\,h, then the average speed of the normal train is:


v_(2) = 90\cdot \left((4\,h)/(10\,h - 4\,h) \right)


v_(2) = 60\,(km)/(h)

The speed of the normal train is 60 kilometers per hour.

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