Question

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

Answer 1

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