SOLUTION: Suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. Suppose also that it takes 200

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Question 1004225: Suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. Suppose also that it takes 200 workers 3 weeks to build 2 miles of highway. How many workers would be needed to build 5 miles of highway in 6 weeks?
Answer by ikleyn(52879) About Me  (Show Source):
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Suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers. Suppose also that it takes 200 workers 3 weeks to build 2 miles of highway. How many workers would be needed to build 5 miles of highway in 6 weeks?
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2%2F%28200%2A3%29 = 5%2F%28x%2A6%29.

This proportion equalize the rate of work in these two cases.

x is unknown number of workers to build 5 miles of highway in 6 weeks.

Solve the proportion for x.

The answer is: x = %28200%2A3%2A5%29%2F%282%2A6%29 = 250 workers.

The way of equalizing the rates is the universal and most direct method to solve problems like this one.