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 long will it take 225 workers to build 27 miles of highway?
We can use the formula for direct and inverse variation, which is:
t = k * (L / w)
where t is the time it takes to build the highway, L is the length of the highway, w is the number of workers, and k is a constant of proportionality.
To solve for k, we can use the given information:
22 = k * (24 / 300)
k = 22 * 300 / 24
k = 275
Now we can use k to solve for the time it takes with different values of L and w. For the new situation where L = 27 miles and w = 225 workers, we have:
t = 275 * (27 / 225)
t = 33
Therefore, it will take 225 workers 33 weeks to build 27 miles of highway.