# Alli can mop Strong Hall in 10 hours. Working together. Alli and Zach mop Strong Hall in 4 hours. How long would it take Zach to do this job alone?

Alli can mop Strong Hall in 10 hours. Working together. Alli and Zach mop Strong Hall in 4 hours. How long would it take Zach to do this job alone?
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Julianna Crawford
Let each would mop the strong hall x hours
Then in 1 hour each can mop $\frac{1}{x}$ of the strong hall
Again similerly if Ali can mop the strong hall in 10 hours.
So in 1 hour Ali alone can mop 1/10 of the strong hall.
Now they together mop the hall in 4 hours
So $4×\left(\frac{1}{x}+\frac{1}{10}\right)=1\phantom{\rule{0ex}{0ex}}\frac{1}{x}+\frac{1}{10}=\frac{1}{4}\phantom{\rule{0ex}{0ex}}\frac{1}{x}=\frac{1}{4}-\frac{1}{10}\phantom{\rule{0ex}{0ex}}\frac{1}{x}=\frac{5-2}{20}⇒\frac{1}{x}=\frac{3}{20}⇒x=\frac{20}{3}\phantom{\rule{0ex}{0ex}}x=6.67$
So each alone would mop the strong hall in 6.67 hours.