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 als

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
100
workers
6
weeks to build
4
miles of highway. How many miles of highway could
160
workers build in
15
weeks?

Answer 1

Time varies directly with length and inversely with number of workers

 

t = kL/w

where k is constant of proportion, L = length, w = # workers

 

100 workers take 6 weeks to build 4 miles

 

6 = 4k/100

Solve for k

k = 600/4 = 150

 

Your equation is:  t = 150L/w

 

Plug into this w=160, t = 15 ...

 

15 = 150L/160   ...   solve for L