Question

The Delaware Demolition Company wants to build a brick wall to hide the area where they store their wrecked cars. One bricklayer can build this wall in 5 days. Another brick layer can do the job in 4 days. If the company hires both of the bricklayers to work together, how long will it take them to complete the wall?

Answer 1

Rate of Brick layer A = 1/5 wall per day

Rate of Brick layer B = 1/4 wall per day

Total rate at which both are working =

$\begin{gathered} \frac{1}{5}+\frac{1}{4} \\ =\frac{4+5}{20} \\ =\frac{9}{20}\text{ wall/day} \end{gathered}$

This implies the rate of the worker is 9/20 of the wall each day

The number of days to complete 1 wall is the inverse of the total rate of walls built per day

$\begin{gathered} =\text{ }\frac{1}{\frac{9}{20}} \\ \\ =\frac{20}{9}\text{ days/wall} \\ or\text{ 2}\frac{2}{9}\text{ days /wall} \\ \\ \text{Hence , it will take them 2}\frac{2}{9}days\text{ to complete the wall} \end{gathered}$