Question

Carl can paint a room 3 hours faster than Jennifer can

If they work together, they can complete the job in 2 hours
Using complete sentences, explain each step in figuring out how to determine the time it would take Jennifer to complete this job on her own.

Answer 1

Jen take x hours.
Carl (x-3)hours.
Jen+carl take two hours;
This means;
In 1 hour, for they work

`(1)/(x) + (1)/(x-3)`
=
`((x-3)+x)/(x(x-3))`
=
`(2x-3)/(x(x-3))`
Working together, they take two hours;
Take reciprocal of above equation and equate to two;
=
`(x(x-3))/(2x-3) =2`

`x^(2)`-3x=4x-6

`x^(2) -7x+6=0`

`x^(2)`-x-6x+6=0
x(x-1)-6(x-1)=0
(x-6)(x-1)=0
Take the bracket x-6=0 so that Carl works positive hours
x-6=0
x=6