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 150 workers 14 weeks to build 12 miles of highway. How many miles of highway could 125 workers build in 21 weeks?

Question

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 150 workers 14 weeks to build 12 miles of highway. How many miles of highway could 125 workers build in 21 weeks?

Answer 1

First, we can set up a proportion using the information given:

(Workers * Weeks) / Miles = Constant

(150 * 14) / 12 = (125 * 21) / x

Now, we can solve for x:

(2100) / 12 = (2625) / x

175 = 2625 / x

175x = 2625

x = 15

Therefore, 125 workers could build 15 miles of highway in 21 weeks.