Chapter 11.5, Problem 19P

It takes yon 12 hours to paint a house, your brother 14 hours, and your sister 10 hours. If all three of you work together, how long will it take you to paint the house?

To determine

To calculate the time taken to paint the house together.

Answer to Problem 19P

The time taken to paint the house together is $3\frac{99}{107}$ hours.

Explanation of Solution

Given information:

The given statement is:

“It takes you $12$ hours to paint a house, your brother $14$ hours, and your sister $10$ hours. If all three of you work together, how long will it take you to paint the house?”

Calculation:

Work done in painting the house in $12$ hours is $\frac{1}{12}$ .

Work done in painting the house in $14$ hours is $\frac{1}{14}$ .

Work done in painting the house in $10$ hours is $\frac{1}{10}$ .

The work done together can be calculated by:

  $\begin{array}{l}\frac{1}{12}+\frac{1}{14}+\frac{1}{10}\\ =\frac{35+30+42}{420}\\ =\frac{107}{420}\end{array}$

The time taken to paint the house together is:

  $\begin{array}{l}1÷\frac{107}{420}\\ =1\times \frac{420}{107}\\ =\frac{420}{107}\\ =3\frac{99}{107}\end{array}$

Hence, the time taken to paint the house together is $3\frac{99}{107}$ hours.