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It takes Conner 15 hours to rake the front lawn while his brother, Devante, can rake the lawn in 9 hours. How long will it take them to take the lawn working together?

User Rbex
by
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1 Answer

4 votes

We know that Conner rakes the front lawn in 15 hours, this means that Conner's rate is:


(1)/(15)

On the other hand, Devante does the work in 9 hours then his rate is:


(1)/(9)

Let x be the time if they do the work together, then their rate is:


(1)/(x)

Hence the sum of their individual rates is equal to the combined rate:


(1)/(15)+(1)/(9)=(1)/(x)

Solving for x we have:


\begin{gathered} (1)/(15)+(1)/(9)=(1)/(x) \\ (9+15)/(135)=(1)/(x) \\ (24)/(135)=(1)/(x) \\ x=(135)/(24) \\ x=5.625 \end{gathered}

Therefore, the time it takes them 5.625 hours to do the job together.

User Gunnm
by
8.6k points
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