Chapter 9.5, Problem 24P

To determine

To find: The time taken by Patrick to do the entire painting job alone.

Answer to Problem 24P

The time taken by Patrick to do the entire painting job alone be 5 hours 20 minutes.

Explanation of Solution

Given information:

Larry takes 8 hours to do the entire job alone.

Larry had already worked for 3 hours before Patrick came.

They together finish the remaining job in 2 hours.

Calculation:

Let, the time taken by Patrick to do the entire painting job alone be x hours.

In 2 hours Patrick can do $\frac{2}{x}$ part of the job

In 2 hours Larry can do $\frac{2}{8}$ part of the job

In 3hoursLarry had done $\frac{3}{8}$ part of the job

By question

  $\begin{array}{l}\frac{2}{x}+\frac{2}{8}+\frac{3}{8}=1\\ \frac{2}{x}=1-\frac{5}{8}\\ \frac{2}{x}=\frac{3}{8}\\ x=\frac{16}{3}\end{array}$

  $\frac{16}{3}$ hours = 5 hours 20 minutes

Therefore, the time taken by Patrick to do the entire painting job alone be 5 hours 20 minutes.