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X works 3 times as fast as Y and is able...

X works 3 times as fast as Y and is able to complete a work in40 days less than the number of days taken by Y. Find the time in which they can complete the work together.

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If Y does the work in 3 days, X does it in 1 day, i.e., the difference is 2 days. But the actual difference is 40 days.
If difference is 2 days, X takes 1 day and Y takes 3 days. If difference is 40 days(i.e., 20 times),
X takes 20 days and Y takes 60 days.
`:.` Time taken together `=(20xx60)/(20+60)=15` days.
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