Calculate work of machines

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This is a GRE question:

Working together, machines A, B, and C can complete a job in 24 hours. Working together, machines B, C, and D can complete the job in 60 hours. If working alone, machine D can complete the job in 120 hours, in how many hours can machine A complete the job when working alone?

Options for the answer are: $16\frac{2}{3}$, $24$, $28$, $30$, and $33\frac{1}{3}$. The correct answer is $30$. Why?

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Hint: Let $A$, $B$, $C$, $D$ represent the number of jobs each machine can do individually per 120 hours.

Then: $$A+B+C={120 \over 24}=5$$ $$B+C+D={120 \over 60}=2$$ $$D={120 \over 120}=1$$

Add the first and third equations to yield $A+B+C+D=6$. Then subtract the second equation to yield $A=4$. So machine A does 4 jobs in 120 hours, so one job takes 30 hours.