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 300 workers 22 weeks to build 24 miles of Highway. how many workers would be needed to build 27 miles of Highway in 33 weeks? __ workers

Answer 1

Since the time is in direct proportion with the length and inverse proportion with the number of workers, then

Let the amount of time is T, the length of the highway is L and the number of workers is N

`(T_1)/(T_2)=(L_1)/(L_2)*(N_2)/(N_1)`

Since

T1 = 22, L1 = 24, N1 = 300

T2 = 33, L2 = 27, N2 = ?

Let us substitute them in the relation above

`(22)/(33)=(24)/(27)*(N_2)/(300)`

Let us simplify it

`\begin{gathered} (2)/(3)=(8)/(9)*(N_2)/(300) \\ (2)/(3)=(8N_2)/(2700) \end{gathered}`

By using cross multiplication

`\begin{gathered} 3(8N_2)=2(2700) \\ 24N_2=5400 \end{gathered}`

Divide both sides by 24

`\begin{gathered} (24N_2)/(24)=(5400)/(24) \\ N_2=225 \end{gathered}`

Then it needs 225 workers to finish the job