Mathematics: Marilyn and Gene are painting a room. Marilyn can paint it in 1 hour less time than Gene. Together they can do the job in 4 hours. How long will it take Gene if he works alone? Give your answer to the nearest tenth

Marilyn and Gene are painting a room. Marilyn

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20.01.2022

Gene can take 0.8 hours to complete work

Step-by-step explanation:

Gene can paint a room in x hours

We are given that Marilyn can paint it in 1 hour less time than Gene

Marilyn can paint a room in (x-1) hours

Gene 1 hour work = $\frac{1}{x}$

Marilyn 1 hour work = $\frac{1}{x-1}$

(Gene and Marilyn)'s 1 day work together= $\frac{1}{x}+\frac{1}{x-1}$

Together they can do the job in 4 hours.

So, their 1 hour work = $\frac{1}{4}$

So, $\frac{1}{x}+\frac{1}{x-1}=\frac{1}{4}$

$\frac{x-1+x}{x(x-1)}=\frac{1}{4}$

4(2x-1)=x^2-x

8x-4=x^2-x

x^2-x-8x+4=0

x^2-9x+4=0

General equation : ax^2+bx+c=0

Formula : $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{9\pm\sqrt{(-9)^2-4(1)(4)}}{21}$

x=0.812,0.0446

So, Gene can take 0.8 hours to complete work

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