Question

Violet were to paint her living room alone it would take three hours. Her sister Fran could do the job in five hours. How many hours would it take them to working together explain your answer as a fraction reduced to lowest terms if needed

Answer 1

Solution:

Given:

$\begin{gathered} Violet=3hrs \\ Fran=5hrs \end{gathered}$

The rates each use to paint one room (living room) is given by;

$\begin{gathered} Violet=\frac{1}{3}room\text{ per hour} \\ Fran=\frac{1}{5}room\text{ per hour} \end{gathered}$

If both work together, their combined rates will be;

$\begin{gathered} \frac{1}{3}+\frac{1}{5}=\frac{5+3}{15} \\ =\frac{8}{15}room\text{ per hour} \end{gathered}$

Hence, the time it will take them to finish painting the room working together is;

$\begin{gathered} \frac{1}{\frac{8}{15}}=1\times\frac{15}{8} \\ =\frac{15}{8}hours\text{ per room} \\ =1\frac{7}{8}hours \end{gathered}$

Therefore, the time it will take them to finish painting the room working together is;

$1\frac{7}{8}\text{ }hours$