Question

4 Sharon can shovel 40 feet of sidewalk in 20 minutes if the snow is 4 inches deep. Shirley needs 30 minutes to do the same job. How long will it take them together to shovel 40 feet of sidewalk with snow 4 inches deep?

Answer 1

Given:

Time Sharon take to complete the task = 20 minutes

Time Shirley take to complete the task = 30 minutes

Therefore:

let x = time it will take both to complete the task

We have the equation:

`(1)/(20)+(1)/(30)=(1)/(x)`

Multiply to both sides by x:

`(x)/(20)+(x)/(30)=(1)/(x)x`

Simplify:

`\begin{gathered} (x\cdot30+x\cdot20)/((20)(30))=1 \\ (30x+20x)/(600)=1 \\ (50x)/(600)=1,\text{ simplify} \\ (x)/(12)=1 \\ 12\cdot(x)/(12)=1\cdot12 \\ x=12 \end{gathered}`

Answer: 12 minutes