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 300 workers 22 weeks to build 24 miles of highway. How many miles of highway could 225 workers build in 33 weeks?
To solve this problem, we can set up a proportion using the given information:
(Workers * Time) / Length = k
Where k is a constant of variation.
Using the given information with 300 workers, 22 weeks, and 24 miles of highway, we have:
(300 * 22) / 24 = k
6600 / 24 = k
k = 275
Now we can use this constant to solve for the length of highway that 225 workers could build in 33 weeks:
(225 * 33) / Length = 275
7425 / Length = 275
Length = 7425 / 275
Length = 27
Therefore, 225 workers could build 27 miles of highway in 33 weeks.