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
$\frac{1}{x} + \frac{1}{x-3}$
=$\frac{(x-3)+x}{x(x-3)}$
=$\frac{2x-3}{x(x-3)}$
Working together, they take two hours;
Take reciprocal of above equation and equate to two;
=$\frac{x(x-3)}{2x-3} =2$
$x^{2}$-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