Question

17.Jim takes 2 times as long as Rosa to clean the garage. Working together, they can clean the garage in 8 hours. How long does it take Jim and Rosa to clean the garage if they work alone? [For full credit, set up an equation and solve it.]

Answer 1

Let t be the time it takes Rosa to clean the garage.

We know that Jim takes two times as long this means that Jim takes 2t to clean the garage.

Now Rosa's rate is given by the amount of garages she cleans divided by the time it takes this means that her rate is 1/t.

Similarly Jim's rate is 1/2t.

We know that working together they take 8 hours, thant their rate together is 1/8.

Therefore we have the equation:

`(1)/(t)+(1)/(2t)=(1)/(8)`

Solving for t we have:

`\begin{gathered} (1)/(t)+(1)/(2t)=(1)/(8) \\ (2t+t)/(2t^2)=(1)/(8) \\ 8(3t)=2t^2 \\ 24t=2t^2 \\ 12t=t^2 \\ t^2-12t=0 \\ t(t-12)=0 \\ \text{then} \\ t=0 \\ or \\ t=12 \end{gathered}`

Since they can't do it in zero hours we conclude that it takes Rosa 12 hours to clean the garage and it takes Jim 24 hours to clean the grarage.