# It takes Noah 3 hours to paint one side of a fence. It takes Gilberto 5 hours. How long would it take them if they worked together?

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To determine how long it would take Noah and Gilberto to paint the fence together, we can use the concept of work rates. Noah takes 3 hours to paint one side of the fence, so his work rate is 1/3 of the fence per hour. Gilberto takes 5 hours, so his work rate is 1/5 of the fence per hour.

To find their combined work rate, we add their individual work rates: 1/3 + 1/5 = 8/15.

Therefore, working together, Noah and Gilberto can paint 8/15 of the fence per hour.

To find the time it would take them to complete the entire fence, we can divide the total work (1) by their combined work rate (8/15):

1 / (8/15) = 15/8 = 1.875 hours.

So, it would take Noah and Gilberto approximately 1.875 hours, or 1 hour and 52.5 minutes, to paint the fence together.

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