Chapter 11.8, Problem 4CYP

To determine

To calculate: The work done in raking leaves by Jenna and her brother together.

Answer to Problem 4CYP

The time required for Jeena and her brother to do the work together is $\frac{6}{5}$ .

Explanation of Solution

Given information:

The required time for Jenna to rake leaves is $2\text{hours}$

The required time for Jenna’s brother to rake leaves is $3\text{hours}$

Formula used:

Work done:

  $work=rate\times time$

Calculation:

Consider work as unity.

Calculate rate of Jenna’s work:

  $\begin{array}{c}rate=\frac{work}{time}\\ =\frac{1}{2}\end{array}$

Calculate rate of Jenna’s brother’s work:

  $\begin{array}{c}rate=\frac{work}{time}\\ =\frac{1}{3}\end{array}$

Calculate the total work.

  $\begin{array}{c}rate\times time=work\\ \left(\frac{1}{2}+\frac{1}{3}\right)t=1\\ \frac{t}{2}+\frac{t}{3}=1\end{array}$

Solve the above equation to find the value of t.

  $\begin{array}{c}\frac{3t+2t}{6}=1\\ 3t+2t=6\\ 5t=6\\ t=\frac{6}{5}\end{array}$

Hence, the time required for Jeena and her brother to do the work together is $\frac{6}{5}$ .