Question

By checking work records, a carpenter finds that Juanita can build a small shed in 13 hours. Anton can do the same job in 20 hours. How long would it take to build 7 sheds if they worked together?It will take them __hour(s) __minute(s) to build 7 sheds together.

Answer 1

Answer:

55 hours 9 minutes

Explanation:

Juanita can build a small shed in 13 hours.

• Juanita's work rate = 1/13

Anton can do the same job in 20 hours.

• Anton's work rate = 1/20

Let the time taken it will take both of them to build a shed = x.

• Then, their joint rate = 1/x.

Thus:

$\frac{1}{13}+\frac{1}{20}=\frac{1}{x}$

First, solve for x:

The LCM of 13 and 20 = 260.

$\begin{gathered} \frac{20+13}{260}=\frac{1}{x} \\ \frac{33}{260}=\frac{1}{x} \\ 33x=260 \\ x=\frac{260}{33}\; hours \end{gathered}$

Since we want to find the time it takes to build 7 sheds if they worked together, multiply x by 7:

$\begin{gathered} 7x=7\times\frac{260}{33} \\ =55\frac{5}{33}\text{ hours} \\ =55\; hours+(\frac{5}{33}\times60)\text{ minutes} \\ =55\; hours\text{ 9 minutes} \end{gathered}$

It will take them 55 hours 9 minutes to build 7 sheds together.​