SOLUTION: The average speed of an express train is 40 km/hr faster than the average speed of a bus. To travel 1200km,the bus requires 50% more time than the train. Determine the average spee

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Question 1054464: The average speed of an express train is 40 km/hr faster than the average speed of a bus. To travel 1200km,the bus requires 50% more time than the train. Determine the average speed of the bus and the train.
Answer by ikleyn(52810) About Me  (Show Source):
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The average speed of an express train is 40 km/hr faster than the average speed of a bus.
To travel 1200 km,the bus requires 50% more time than the train. Determine the average speed of the bus and the train.
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Let x = the bus speed, in km%2Fh.
Then the train speed is (x+40) km%2Fh.

The time for the bus to cover 1200 km is 1200%2Fx.
The time for the train is 1200%2F%28x%2B40%29.

We are given that

1.5%2A%281200%2F%28x%2B40%29%29 = 1200%2Fx.

Cancel the factor 1200 in both sides. You will get

1.5%2F%28x%2B40%29 = 1%2Fx.

Multiply both sides by x*(x+40). You will get

1.5x = x+40  --->  0.5x = 40  --->  x = 40%2F0.5 = 80 km%2Fh.

It is the bus speed. Then the trai speed is 40 km%2Fh more, i.e. 120 km%2Fh.

Answer.  The train speed is 120 km/h.  The bus speed is 80 km/h.