Question

Round the answer by the nearest hundred.Working alone, Mark can tar a roof in 9 hours. Ashley can tar the same roof in 15 hours. How long would it take them if they worked together?

Answer 1

Given:

$\begin{gathered} Mark(tar-a-roof)=9hours \\ Ashley(tar-a-roof)=15hours \end{gathered}$

To determine: How long it will take Mark and Ashley to a roof

Solution

Let us determine the unit of roof tar by Mark and Ashley in one hour

$\begin{gathered} Mark(unit-tar-in-1hour)=\frac{1}{9} \\ Ashley(unit-tarred-in-1hour)=\frac{1}{15} \\ Mark&Ashley(unit-tarred-in-1hour)=\frac{1}{9}+\frac{1}{15}=\frac{5+3}{45}=\frac{8}{45} \end{gathered}$

Therefore, the time it will take them to tar a roof would be as calculated below if it took them x hours

$\begin{gathered} \frac{8}{45}\times x=1 \\ \frac{8x}{45}=1 \\ 8x=45 \\ x=\frac{45}{8} \\ x=5.625 \\ x=5.63hours \end{gathered}$

Hence, it will take both of them approximately 5.63 hours to tar the roof