Problema Solution

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 if workers. Suppose also that it takes 100 workers 6 weeks to build 4 miles of highway. How long will it take 160 workers to build 16 miles of highway

Answer provided by our tutors

let


t = the number of weeks it takes to build the highway

w = the number of workers

d = the length of the highway


the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number if workers


t = k*(l/w), where k is constant


for w = 100 workers, d = 4 miles, t = 6 weeks that is


6 = k(4/100)


k/25 = 6


k = 25*6


k = 150


the formula now is


t = 150(d/w)


if w = 160 workers and d = 16 miles we have


t = 150*(16/160)


t = 150/10


t = 15 weeks


It will take 15 weeks to build 16 miles highway and 160 workers working on it.