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 100 workers 6 weeks to build 4 miles of highway. How long will it take 160 workers to build 16 miles of highway?
First, we can set up a proportion based on the given information:
(Workers x Weeks) / Miles = Constant
Using the information given, we can calculate the constant:
(100 workers x 6 weeks) / 4 miles = Constant
600 / 4 = Constant
Constant = 150
Now, we can use this constant to determine how long it will take 160 workers to build 16 miles of highway:
(160 workers x Weeks) / 16 miles = 150
160 Weeks / 16 = 150
10 Weeks = 150
It will take 160 workers 10 weeks to build 16 miles of highway.