Alex and Billie were busily emptying their book shelves from one room to another.
Alex on their own could have cleared the room in 18 hours.
Billie 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?
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How many rooms could Alex clear in 36 hours?
In 36 hours Alex can clear 2 rooms, Billie can also clear 2 rooms, and Drew would fill 1 room. So 2 + 2 - 1 = 3 rooms in 36 hours. Which is 12 hours for a single room.
Alex and Billie 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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