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 a hundred and fifty workers 14 weeks to build 12 miles of Highway. how many workers would be needed to build 15 miles of Highway in 21 weeks? __ number of workers

Answer 1

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?

Let x denotes the unknown number of workers.

Then we can set up the following equation

`\begin{gathered} w_1* t_1* l_1=w_2* t_2* l_2 \\ w_1* t_1* l_1=x* t_2* l_2 \\ x=(w_1* t_1* l_1)/(t_2* l_2) \\ x=(150*14*12)/(15*21) \\ x=(25200)/(315) \\ x=80 \end{gathered}`

Therefore, 80 workers will be required.