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 long will it take 125 workers to build 15 miles of highway?

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 long will it take 125 workers to build 15 miles of highway?

Answer 1

We can start by using the formula:

time = k * (length of highway / number of workers)

where k is a constant of proportionality.

We can solve for k using the information given in the problem. When 150 workers build a 12-mile highway in 14 weeks, we can plug in those values and get:

14 = k * (12 / 150)

Solving for k, we get:

k = 14 * 150 / 12

k = 175

Now we can use this value of k to answer the question. If 125 workers build a 15-mile highway, the time it takes can be found using the same formula:

time = 175 * (15 / 125)

time = 21 weeks

So it will take 125 workers 21 weeks to build a 15-mile highway.