If one small rabbit can dig a warren in nine hours, a medium rabbit can dig a warren in 6 hours, and a large rabbit can dig a warren in four and a half hours.
How long will it take one small, one medium, and one large rabbit, to dig a warren if they all work together?
Puzzle Copyright © Kevin Stone
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Answer
2 hours.
Reasoning
The small rabbit can dig a warren in nine hours, so digs 1⁄9 in one hour.
The medium rabbit can dig a warren in 6 hours, so digs 1⁄6 in one hour.
The large rabbit can dig a warren in four and a half hours, so digs 1⁄4.5 in one hour.
1 Hour = 1⁄9 + 1⁄6 + 1⁄4.5
To make the denominators all the same, we can multiply through by 18⁄18 to give:
1 Hour = 2⁄18 + 3⁄18 + 4⁄18
1 Hour = 9⁄18
1 Hour = 1⁄2
So in one hour, they have dug half a warren, the whole warren will therefore take 2 hours.