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Puzzle Details

Alex and Blake were busily emptying their book shelves from one room to another.

Alex on their own could have cleared the room in 18 hours.

Blake also would take 18 hours.

Unfortunately, Drew was moving the books back into the first room from the second.

They could fill the first room in 36 hours.

How long will it take the three of them to complete the task?

Puzzle Copyright © Kevin Stone

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Answer: 12 hours.

In 36 hours Alex can clear 2 rooms, Blake can also clear 2 rooms, whilst Drew would fill 1 room. So 2 + 2 - 1 = 3 rooms in 36 hours. Which is 12 hours for a single room.

Alternatively:

Alex and Blake each clear 1/18 of the room in 1 hour, but Drew is filling 1/36 of the room in one hour. So in one hour we have 1/18 + 1/18 - 1/36 = 1/12. So it takes 12 hours to complete the task.

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