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n200080 [17]
3 years ago
10

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 hour

s. How long will it take Gene if he works alone? Give your answer to the nearest tenth
Mathematics
1 answer:
erastovalidia [21]3 years ago
7 0

Answer:

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=\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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