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:
[tex]\frac{1}{20}+\frac{1}{30}=\frac{1}{x}[/tex]Multiply to both sides by x:
[tex]\frac{x}{20}+\frac{x}{30}=\frac{1}{x}x[/tex]Simplify:
[tex]\begin{gathered} \frac{x\cdot30+x\cdot20}{(20)(30)}=1 \\ \frac{30x+20x}{600}=1 \\ \frac{50x}{600}=1,\text{ simplify} \\ \frac{x}{12}=1 \\ 12\cdot\frac{x}{12}=1\cdot12 \\ x=12 \end{gathered}[/tex]Answer: 12 minutes
