An algebra problem by Larisa Altshuler
Two cars departed simultaneously from point A and B toward each other. In seven hours the distance between them was 136 miles. Find the distance between A and B in miles if the car moving from A can cover this distance for 10 hours and the car moving from B can cover this distance for 12 hours.
The answer is 480.
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1 solution
Let D be the distance between A and B. The car from A is moving with the average speed of D/10 mph and for 7 hours covered 7D/10 miles. The second car is moving with the average speed of D/12 mph and in 7 hours covered 7D/12 miles. Both of them for 7 hours covered 77D/60. But, pay attention, it is more than entire distance from A to B (!). That means than the cars passed each other and in 7 hours the car from B is closer to A than the car from A. Thus the distance between two cars in 7 hours is 77D/60 - D. Solving equation 17D/60 = 136, we have the answer D = 480 miles.