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.
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.
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