Sam can do a job in x hours. Denise can do the same job in x+2 hours. How long will it take Sam and Denise to do the job together? (Express answer in terms of x)
My work: 1/x=1/x+(1/(x+2))
..but where do I go from there?
rate sam works ... (1 job)/(x hrs)
rate denise works ... (1 job)/(x+2 hrs)
rate together ... $\displaystyle \frac{1}{x} + \frac{1}{x+2}$
let $\displaystyle t$ = time to do the job together ...
$\displaystyle \left(\frac{1}{x} + \frac{1}{x+2}\right) \cdot t = 1$ job done
solve for t in terms of x