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?

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Hint

How much of a warren each rabbit dig in one hour?

Answer

2 hours.

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.

1/9 + 1/6 + 1/4.5 = 0.5. So in one hour, they have dug half a warren between them, the whole warren will therefore take 2 hours.