Chapter 11.8, Problem 22PPS

To determine

To calculate: the time taken to finish all the plates if they work together.

Answer to Problem 22PPS

The time taken to finish all the plates is $\frac{9}{7}$ hours or $1\frac{2}{7}$ hours.

Explanation of Solution

Given:

R can finish the work in $2$ hours $15$ minutes.

C can finish the work in $3$ hours.

Calculation:

The objective is to calculate the time taken to finish all the plates if they work together.

At first find the rate.

So, $2\frac{1}{4}$ and $\frac{1}{3}$

Let, $t$ be the time.

The required time is calculated below.

  $\begin{array}{l}\frac{1}{2\frac{1}{4}}t+\frac{1}{3}t=1\\ \frac{4}{9}t+\frac{1}{3}t=1\\ \frac{4t+3t}{9}=1\\ 7t=9\\ t=\frac{9}{7}\\ t\approx 1\frac{2}{7}\end{array}$

Therefore, the time is $\frac{9}{7}$ hours or $1\frac{2}{7}$ hours.

Conclusion:

Therefore, the time taken to finish all the plates is $\frac{9}{7}$ hours or $1\frac{2}{7}$ hours.