Chapter 11.8, Problem 21PPS

To determine

To calculate: the time taken to pain the fence if they work together.

Answer to Problem 21PPS

The time taken to pain the fence is $\frac{15}{8}$ hours or $1\frac{7}{8}$ hours.

Explanation of Solution

Given:

N takes $3$ hours to paint one side of a fence.

G takes $5$ hours to paint one side of a fence.

Calculation:

The objective is to calculate the time taken to pain the fence if they work together.

At first find the rate.

So,

  $\frac{1}{3}$ and $\frac{1}{5}$

Let, $t$ be the time.

The required time is calculated below.

  $\begin{array}{l}\frac{1}{3}t+\frac{1}{5}t=1\\ \frac{5t+3t}{15}=1\\ 8t=15\\ t=\frac{15}{8}\\ t\approx 1\frac{7}{8}\end{array}$

Therefore, the time is $\frac{15}{8}$ hours or $1\frac{7}{8}$ hours.

Conclusion:

Therefore, the time taken to pain the fence is $\frac{15}{8}$ hours or $1\frac{7}{8}$ hours.