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} (1)/(5)+(1)/(4) \\ =(4+5)/(20) \\ =(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{ }(1)/((9)/(20)) \\ \\ =(20)/(9)\text{ days/wall} \\ or\text{ 2}(2)/(9)\text{ days /wall} \\ \\ \text{Hence , it will take them 2}(2)/(9)days\text{ to complete the wall} \end{gathered}`