Chapter 9.2, Problem 46SR

To determine

To find: The time duration that will take by both to do the job together.

Answer to Problem 46SR

The time duration that will take by both to do the job together is $2\text{hours13minutes20seconds}$ .

Explanation of Solution

Given:

A worker can do the job in $5$ hours.

Another worker can do the job in $4$ hours

Let the time taken by the workers when they work together is $x$ hours.

So the work done by both the workers together in $1$ hour is $\frac{1}{x}$ .

The work done by the first worker in $1$ hour is $\frac{1}{5}$ .

The work done by the second worker in $1$ hour is $\frac{1}{4}$ .

So the work done by both the workers together in $1$ hour is $\frac{1}{x}$ equated as:

  $\begin{array}{c}\frac{1}{4}+\frac{1}{5}=\frac{1}{x}\\ 20\cdot \frac{1}{4}+20\cdot \frac{1}{5}=20\cdot \frac{1}{x}\left[\text{multiply by 20}\right]\\ 9=\frac{20}{x}\\ x=\frac{20}{9}\end{array}$

So the hours spend by both the worker together to do the job is:

  $\frac{20}{9}=2\text{hours13minutes20seconds}$ .

Therefore the time duration that will take by both to do the job together is $2\text{hours13minutes20seconds}$