Difference in Distances over Time

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Cyclist A averages 19.9 miles per hour and Cyclist B averages 15.1 miles per hour. If each cycle is ridden 1,500 miles, approximately how many more hours will Cyclist B ride than Cyclist A?

Review: Difference in Distances over Time


Explanation

This computation looks beastly, but the question says "approximately," so we can take the speed of A to be 20 miles per hour and that of B to be 15 miles per hour. (When we get to the stage of evaluating the answers, we'll recall that we approximated and question whether we have answered precisely enough.)Cyclist A rides at a constant rate of . Without changing the rate, we want to get it to express the time for 1500 miles. To do this, we can multiply the fraction by 1:



So, A will take hours. B will take hours, which is more, because the denominator is smaller. It's easy enough to compute directly, but I would prefer to use the common denominator of 60:







Our estimate is 25.

The correct answer is (C).


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