Question

A group of college students are volunteering for help the homeless during their spring break. they are putting the finishing touches on a house they built. working alone, irina can paint a certain room in 7 hours. paulo can paint the same room in 6 hours. choose the equation that can be used to find how long it will take them working together to paint the room. how many hours will it take them to paint the room? if necessary, round your answer to the nearest hundredth.

Answer 1

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Irina:
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Irina takes 7 hours to paint the room.
In 1 hour, Irina can paint 1/7 of the room.

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Paulo:
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Paulo takes 6 hours to paint the room.
In 1 hour, Paulo can paint 1/6 of the room.

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Both paint together:
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In one hour they can paint (1/7 + 1/6) of the room.
1/7 + 1/6 = 13/42

So, it takes 13/42 of the room takes 1 hour.

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Find the number of hours
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13/42 of the room = 1 hour

Whole room = 1 ÷ 13/42
Whole room = 1 x 42/13
Whole room = 3.23 hours

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Answer: They need 3.23 hours to paint the room.
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