Chapter 8, Problem 52SGR

To determine

To find: How long will it take them if they work together.

Answer to Problem 52SGR

They will take 1.714 hours to complete it together.

Explanation of Solution

Given information:

Lana can plant a garden in 3 hours. Milo can plant the same garden in 4 hours.

Calculation:

Since Lana can plant the garden in 3 hours. Therefore,

The rate for Lana is $\frac{1}{3}$ of a garden per hour.

The rate for Milo is $\frac{1}{4}$ of a garden per hour.

Let they take $x$ hour to complete it together. Therefore,

The combined rate is $\frac{1}{x}$ .

Thus,

  $\begin{array}{l}\frac{1}{3}+\frac{1}{4}=\frac{1}{x}\\ \frac{4+3}{12}=\frac{1}{x}\\ \frac{7}{12}=\frac{1}{x}\\ x=\frac{12}{7}\\ x=1.714\end{array}$

Hence,

They will take 1.714 hours to complete it together.