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# help

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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?

May 18, 2020

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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)

May 18, 2020