Question

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?

Answer 1

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.