Chapter 9.6, Problem 24PPS

To determine

To find : how long would it take them if they worked together

Answer to Problem 24PPS

  $6.86\text{ hours}$ time would take them if they worked together

Explanation of Solution

Given information :

Bryan’s volunteer group can build a garage in 12 hours. Sequoia’s group can build it in 16 hours.

Calculation :

Bryan’s volunteer group can build a garage in 12 hours

Bryan’s volunteer group can build a garage in 1 hours $=\frac{1}{12}$

Sequoia’s group can build it in 16 hours

Sequoia’s group can build it in 1 hours $=\frac{1}{16}$

Time would take them if they worked together

  $\begin{array}{l}\frac{1}{12}+\frac{1}{16}\\ =\frac{1\cdot 4+1\cdot 3}{48}\\ =\frac{4+3}{48}\\ =\frac{7}{48}\end{array}$

Therefore, 7 garage are built by together in 48 hours.

Therefore, 1 garage is built by together

  $\begin{array}{l}=\frac{48}{7}\text{ hours}\\ =6.86\text{ hours}\end{array}$

Hence, $6.86\text{ hours}$ time would take them if they worked together.