X can do a job in three days. If X and Y together can do the job in two days, and Y works twice as fast as Z, then X and Z can do the job in how many days?
The amount of the job that X can do in one day is \(\frac{1}{3}\). Let's call the amount of the job Y can do in one day \(\frac{1}{y}\). Then the amount of job Z can do is \(\frac{1}{2y}\)(half of \(\frac{1}{y}\)).
The expression we want is \(\frac{1}{\frac{1}{3}+\frac{1}{2y}}\)(the best way to get this is to solve for \(y\)).
From our information, we have that \(\underbrace{\frac{1}{3}+\frac{1}{y}}_{\text{amount of work X and Y can do in one day}}=\underbrace{\frac{1}{2}}_{\text{amount of work done in one day}}\)(it takes them 2 days to get the job done)
Solving for y, we see that \(y=6\) (to solve just multiply both sides by 6y)
So X and Z can do the job in \(\frac{1}{\frac{1}{3}+\frac{1}{2y}}=\frac{1}{\frac{1}{3}+\frac{1}{12}}=\frac{1}{\frac{5}{12}}=\frac{12}{5}\) days.
(Please check my work, I'm not sure if 12/5 is actually the answer)
