Jen take x hours.
Carl (x-3)hours.
Jen+carl take two hours;
This means;
In 1 hour, for they work
[tex] \frac{1}{x} + \frac{1}{x-3} [/tex]
=[tex] \frac{(x-3)+x}{x(x-3)} [/tex]
=[tex] \frac{2x-3}{x(x-3)} [/tex]
Working together, they take two hours;
Take reciprocal of above equation and equate to two;
=[tex] \frac{x(x-3)}{2x-3} =2[/tex]
[tex] x^{2} [/tex]-3x=4x-6
[tex] x^{2} -7x+6=0[/tex]
[tex] x^{2} [/tex]-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
