Howard T.

asked • 07/02/19

Train question from math homework

If a train is moving at 40 mph headed northeast and a bus is headed towards it at a 30 degree angle at 55 miles per hour, if both start out 50 miles apart how many minutes will it take before they intersect?

Mark H.

This is ambiguous. if the 30 degree angle is relative to the motion of the train, then the direction of the train is irrelevant. But there are still 2 possibilities for the direction of the direction of the bus
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07/02/19

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Patrick B. answered • 07/02/19

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The motion of the train is 45 above the x-axis.

THe motion of the bus is 30 above the x-axis.


So triangle ABC, A on the left, B on top, C on the right.

A is 45, B is 105, C is 30.


AC=50, AB = y and BC = x


law of sines says:


sin 45/ x = sin 105/ 50 = sin 30/y

then x = 36.60254+....

and y = 25.8819045+


at the given speeds, they will intersect between 39 and 40 minutes

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