### Brain Teasers

# Digging Rabbits

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?

### Answer

2 hours.In one hour, each rabbit can dig 1/9, 1/6, and 1/4.5 of a warren, respectively. To figure out how much the three of them can do in an hour, just add these up (convert to 18ths first):

2/18 + 3/18 + 4/18 = 9/18 = 1/2. Since together they can dig half of a warren per hour, it will take two hours to dig a whole warren.

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