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Harry, Annie and Mitch decided to paint the living room.Harry could paint the room by himself in 3 hours.Annie could do it in 4 hours and Mitch would take 6 hours on his own.If they all work together and don't get in each other's way, how long will the job take?

Question

Harry, Annie and Mitch decided to paint the living room.Harry could paint the room by himself in 3 hours.Annie could do it in 4 hours and Mitch would take 6 hours on his own.If they all work together and don't get in each other's way, how long will the job take?

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Solution

First, we need to determine how much of the room each person can paint in one hour.

Harry can paint the room in 3 hours, so he can paint 1/3 of the room in one hour.

Annie can paint the room in 4 hours, so she can paint 1/4 of the room in one hour.

Mitch can paint the room in 6 hours, so he can paint 1/6 of the room in one hour.

If they all work together, we can add up the fractions of the room they can paint in one hour to find out how much of the room they can paint together in one hour.

1/3 + 1/4 + 1/6 = 4/12 + 3/12 + 2/12 = 9/12 = 3/4

So, together, they can paint 3/4 of the room in one hour.

To find out how long it will take them to paint the whole room, we divide the whole room (1) by the fraction of the room they can paint in one hour (3/4).

1 ÷ 3/4 = 1.33 hours

So, it will take them approximately 1.33 hours to paint the room together.

This problem has been solved

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