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

4 hours

Explanation:

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

`(1)/(5)`

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

`(1)/(20)`

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

`(1)/(x)`

Therefore:

`(1)/(5)+(1)/(20)=(1)/(x)`

We solve the equation for x:

`\begin{gathered} (4+1)/(20)=(1)/(x) \\ (5)/(20)=(1)/(x) \\ \text{ Cross multiply} \\ 5x=20 \\ \text{ Divide both sides by 5} \\ (5x)/(5)=(20)/(5) \\ x=4\text{ hours} \end{gathered}`

It takes them 4 hours to build a wall together.