Question

Sally can paint the office by herself in 10 hours. Dave can do the same job in 7 hours. How long will it take if they do it working together? Answer in fraction.

Answer 1

The answer is 70/17 hours.

Given:

The time required by Sally to paint is, S = 10 hours.

The time required byDave to paint is, D = 7 hours.

The objective is to find the number of hours it will take if they do it working together.

Work done by Sally in 1 hour can be calculated as,

$\begin{gathered} 10\text{ hours = 1 work} \\ 1\text{ hour=}\frac{1}{10}work \end{gathered}$

Work done by Dave in 1 hour can be calculated as,

$\begin{gathered} 7\text{ hours=1 work} \\ 1\text{ hour=}\frac{1}{7}work \end{gathered}$

The work completed by both together in 1 hour can be calculated as,

$\begin{gathered} W(1)=\frac{1}{10}+\frac{1}{7} \\ =\frac{7+10}{7\cdot10} \\ =\frac{17}{70} \end{gathered}$

Now, the time required to complete the work together can be calculated as,

$\begin{gathered} T=\frac{1}{W(1)} \\ =\frac{1}{\frac{17}{70}} \\ =\frac{70}{17} \end{gathered}$

Hence, the time required to complete the work together is 70/17 hours.