Monday, May 11, 2009

Speed Problem...Again

A car needs 7 hours to travel from Town X to Town Y. A motorcycle needs 8 hours to travel from Town Y to Town X. The car leaves Town X for Town Y and the motorcycles leaves from Town Y to Town X at the same time. How long will it take for the car and the motorcycle to meet?
Speed Problems are frequently brought up. There are earlier entries discussing Speed Problems. See below.
So, how long will it take for the car and the motorcyle to meet. The standard joke is that we hope they don't!
That aside, we need to assume that the speed of the two vehicles are constant. If that is so then in an hour, the car travels 1/7 the distance in an hour and the motorcycle travels 1/8 the distance in an hour. The problem is solved when the distance travelled by the car and motorcyle add up to 1 whole. In an hour, total distance covered by both is (1/7 + 1/8) of XY. This works out to 15/56 of XY. In 2 hours, it is (2/7 + 2/8) of XY or 30/56 of XY. In 3 hours, 45/56. In 4 hours, 60/56. They would have passed each other in 4 hours. Can I leave it to you to complete the last step of the solution. It is by no means trivial but there are enough leads already.

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