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 many miles of highway could 160 workers build in 15 weeks?

Answer 1

First, we can set up a proportion to find the constant of variation:

(Workers) x (Time) = (Highway length)
100 x 6 = 4
(Workers) x 15 = (Highway length)
160 x 15 = Highway length

Thus, to find the highway length that 160 workers could build in 15 weeks, we can use the proportion:

(100 x 6)/(160 x 15) = 4/x
600/2400 = 4/x
1/4 = 4/x
x = 16

Therefore, 160 workers could build 16 miles of highway in 15 weeks.