albiguguiismx

2022-09-14

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?

Julianna Crawford

Beginner2022-09-15Added 8 answers

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 $$4\times (\frac{1}{x}+\frac{1}{10})=1\phantom{\rule{0ex}{0ex}}\frac{1}{x}+\frac{1}{10}=\frac{1}{4}\phantom{\rule{0ex}{0ex}}\frac{1}{x}=\frac{1}{4}-\frac{1}{10}\phantom{\rule{0ex}{0ex}}\frac{1}{x}=\frac{5-2}{20}\Rightarrow \frac{1}{x}=\frac{3}{20}\Rightarrow x=\frac{20}{3}\phantom{\rule{0ex}{0ex}}x=6.67$$

So each alone would mop the strong hall in 6.67 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 $$4\times (\frac{1}{x}+\frac{1}{10})=1\phantom{\rule{0ex}{0ex}}\frac{1}{x}+\frac{1}{10}=\frac{1}{4}\phantom{\rule{0ex}{0ex}}\frac{1}{x}=\frac{1}{4}-\frac{1}{10}\phantom{\rule{0ex}{0ex}}\frac{1}{x}=\frac{5-2}{20}\Rightarrow \frac{1}{x}=\frac{3}{20}\Rightarrow x=\frac{20}{3}\phantom{\rule{0ex}{0ex}}x=6.67$$

So each alone would mop the strong hall in 6.67 hours.

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