Approaching Cars

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Car A and Car B are driving toward each other along a straight line. Car A travels at a constant speed of 60 miles per hour and Car B travels at a constant speed of 40 miles per hour. If at noon they are separated by a distance of 300 miles, at what time will they meet?

Review: Approaching Cars


Explanation

This question is more of a combined rate question than a speed question. We care only indirectly about the individual speeds of the cars and directly about how quickly the gap between the cars closes. In fact, the distance between the cars is closing at a rate of miles per hour. Since the distance is initially 300 miles, it will therefore take three hours to close the gap. They begin at noon, so they meet at three o'clock. The correct answer is (B).

As you can see, the combined rate approach to this question is incredibly swift. You could solve the question by constructing three equations with the speed formula, but it's fairly laborious. To be sure to take advantage of the opportunity to use combined rates whenever it's at hand, take note whenever a question has more than one rate. If there's more than one speed or other rate, those multiple rates possibly can be added or subtracted.

Again, the correct answer is (B).


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