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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

User Toinbis
by
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1 Answer

3 votes

Answer:

Gene can take 0.8 hours to complete work

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 =
(1)/(x)

Marilyn 1 hour work =
(1)/(x-1)

(Gene and Marilyn)'s 1 day work together=
(1)/(x)+(1)/(x-1)

Together they can do the job in 4 hours.

So, their 1 hour work =
(1)/(4)

So,
(1)/(x)+(1)/(x-1)=(1)/(4)


(x-1+x)/(x(x-1))=(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=(-b\pm√(b^2-4ac))/(2a)


x=(9\pm√((-9)^2-4(1)(4)))/(21)


x=(9\pm√((-9)^2-4(1)(4)))/(21)

x=0.812,0.0446

So, Gene can take 0.8 hours to complete work

User DeeveeABC
by
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