Question

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 150 workers 14 weeks to build 12 miles of Highway. how many workers would be needed to build 15 miles of Highway in 21 weeks? __workers

Answer 1

Let t represent the amount of time required

Let l represent the length of the highway

Let n represent the number of workers

Let k represent the constant of proportionality.

If the amount of time it takes to build a highway varies directly with the length of the highway, then the relationship would be

t = kl

If the amount of time it takes to build a highway varies inversely with the number of workers, then the relationship is

t = k/n

If we combine both equations, the we would have

t = kl/n

If it takes 150 workers 14 weeks to build 12 miles of Highway, then

n = 150, t = 14 and l = 12

Substituting these values into the equation, we have

14 = k * 12/150

14 = 0.08k

k = 14/0.08

k = 175

Thus, the equation is

t = 175l/n

Thus, if l = 15, t = 21, then the number of workers needed, n would be

21 = 175 * 15/n

21n = 2625

n = 2625/21

n = 125

Thus, 125 workers would be needed to build 15 miles of Highway in 21 weeks