### 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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## Comments

Isn't this basically if man and a half can dig a hole and a half...

well, that is sorta a good one

What i did was...trial and error..my first instint was 2 hours so i took 2 and divided by # of hours each took. ex. small takes 9 hours so its 2/9..then i took the percentage of that and did that for the other two. It came up to 99% when i added the 3 together so i guess thats correct.

This was really easy. You just have to add some fractions to figure out how much of a warren they can dig in one hour.

An easy way to think about it (9, 6 and 4.5 divide into 1 is to imagine that a warren contains 18 cubic metres of dirt. Rabbit A digs 2 cum/hr, Rabbit B digs 3 cum/hr and rabbit C digs 4 cum/hr. Altogether they dig 9 cum/hr so it takes 2 hours.

Good Teaser.

Good Teaser.

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