Chapter 14, Problem 7MPS

To determine

To Find: The time at which the job is finished.

Answer to Problem 7MPS

The job is finished at at13:08 PM.

Explanation of Solution

Given:

The time taken to split the cord of wood is 7 hour.

The time taken by Meg to do the job is 5 h.

The time at which the Rachel began the job is 9:00 AM and the time at which the Meg joined is 11:00 Am.

Calculation:

Consider the time taken by the first person to work is $t$ , the number then the number of hours taken by the second person to work is $t-2$ .

The part of the job that can be done by the first person in one hour is $\frac{1}{7}$ and the part of the job that can be done by the second person is $\frac{1}{5}$ .

Thus, the part of the job that can be done by the first person is $t$ hours is $\frac{t}{7}$ and by the second person is $\frac{t-2}{5}$ .

Consider the equation for the complete job is,

  $\begin{array}{l}35\left(\frac{t-2}{5}+\frac{t}{7}\right)=35\\ 5t+7\left(t-2\right)=35\\ 12t-14=35\\ t=4.08\end{array}$

Thus. The job is finished after $9:00+4:08$ that is at13:08.

Thus, the job is finished at at13:08 PM.