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 that it takes 100 workers 6 weeks to build 4 miles of Highway. how long will it take a 160 workers to build 16 miles of Highway?___weeks

Answer 1

The amount of time it would take 160 workers to build 16 miles of Highway is;

`15\text{ weeks}`

Step-by-step explanation:

Given 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.

Let t represent the time in weeks, l represents the length of the highway in miles, and n represent the number of workers;

So, we have;

`\begin{gathered} t\propto(l)/(n) \\ t=k(l)/(n) \\ k=(nt)/(l) \end{gathered}`

Given;

it takes 100 workers 6 weeks to build 4 miles of Highway

`\begin{gathered} n=100 \\ t=6 \\ l=4 \\ k=(nt)/(l) \\ k=(100*6)/(4) \\ k=150 \end{gathered}`

so, for 160 workers to build 16 miles of Highway the time it will take is;

`\begin{gathered} n=160 \\ l=16 \\ k=150 \\ t=k(l)/(n) \\ t=150*(16)/(160) \\ t=(150)/(10) \\ t=15 \end{gathered}`

Therefore, the amount of time it would take 160 workers to build 16 miles of Highway is;

`15\text{ weeks}`