Question

Mike an experienced bricklayer can build a wall in 5 hours while his son, who is learning can do the job in 20 hours. How long does it take for them to build a wall together.

Answer 1

Answer:

4 hours

Explanation:

Mike can build a wall in 5 hours. His work rate is:

$\frac{1}{5}$

His son can do the job in 20 hours. The son's work rate is:

$\frac{1}{20}$

Let the time it takes both of them = x hours. Then, their joint rate is:

$\frac{1}{x}$

Therefore:

$\frac{1}{5}+\frac{1}{20}=\frac{1}{x}$

We solve the equation for x:

$\begin{gathered} \frac{4+1}{20}=\frac{1}{x} \\ \frac{5}{20}=\frac{1}{x} \\ \text{ Cross multiply} \\ 5x=20 \\ \text{ Divide both sides by 5} \\ \frac{5x}{5}=\frac{20}{5} \\ x=4\text{ hours} \end{gathered}$

It takes them 4 hours to build a wall together.