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.