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it takes Joan two times longer than Jane to file the reports.  together they can file the reports in six minutes. how long will it take each woman to file the reports herself

Respuesta :

Work problems can be express as :

[tex](\frac{1}{a}+\frac{1}{b})t=1[/tex]

where a and b are the rates of two person doing one work

and

t = time to finish the work when working together.

From the problem, Joan takes two times longer than Jane.

If Jane can file the report in x minutes, Joan will be 2x minutes.

They can file the report together in 6 minutes so t = 6

Plug in the values to the equation :

[tex](\frac{1}{x}+\frac{1}{2x})\times6=1[/tex]

Simplify then solve for x :

[tex]\begin{gathered} (\frac{1}{x}+\frac{1}{2x})\times6=1 \\ \text{Multiply both sides by 2x} \\ 2x\times(\frac{1}{x}+\frac{1}{2x})\times6=2x\times1 \\ (2+1)\times6=2x \\ 3\times6=2x \\ 18=2x\text{ } \\ x=\frac{18}{2}=9 \end{gathered}[/tex]

x = 9, so Jane can file the report in 9 minutes.

Since Joan is two times longer than Jane, she can file the report in 18 minutes.

Answers :

Jane = 9 minutes

Joan = 18

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