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:

$\frac{1}{15}$

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

$\frac{1}{9}$

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

$\frac{1}{x}$

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

$\frac{1}{15}+\frac{1}{9}=\frac{1}{x}$

Solving for x we have:

$\begin{gathered} \frac{1}{15}+\frac{1}{9}=\frac{1}{x} \\ \frac{9+15}{135}=\frac{1}{x} \\ \frac{24}{135}=\frac{1}{x} \\ x=\frac{135}{24} \\ x=5.625 \end{gathered}$

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