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?
First, we can set up a proportion to find the constant of variation:
200 workers * 3 weeks = k * 2 miles
k = (200 workers * 3 weeks) / 2 miles
k = 300 workers/week per mile
Now we can use this constant to find out how many workers would be needed to build 5 miles of highway in 6 weeks:
300 workers/week per mile = x workers / 6 weeks * 5 miles
x = (300 workers * 6 weeks * 5 miles) / 1 week
x = 9000 workers
Therefore, 9000 workers would be needed to build 5 miles of highway in 6 weeks.