SOLUTION: Bob and Sarah need to paint a fence. Bob can paint a fence in 4 hours and Sarah can paint a fence in 2.5 hours. If they work together, how long will it take them to paint the fence

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Question 1097855: Bob and Sarah need to paint a fence. Bob can paint a fence in 4 hours and Sarah can paint a fence in 2.5 hours. If they work together, how long will it take them to paint the fence?
Found 3 solutions by josgarithmetic, addingup, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!

Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website!
Bob: in 4 hours 1 fence, in 1 hour 1/4 fence
Sarah: 2.5 hrs to paint the fence, in 1 hour 1/2.5
1/4+1/2.5 = 5/20+8/20 = 13/20
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Ok, now let's call the time it will take them together t:
They will do 1 fence in t time: 1/t. Flip the equation and you get:
1/t = t/1 = 20/13 = 1 hour and 7/13 minutes = or 1 hour and 32.31 minutes or 1 hour 32 minutes and 19 seconds

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

Here is an alternative method that I see many students preferring over the method shown in the two previous responses.

(1) Multiply the times it takes the two of them alone to do the job:

In 10 hours, Bob could paint 2.5 of those fences, and Sarah could paint 4 of them. So in 10 hours the 2 of them together could paint 6.5 fences.

Then the number of hours they would need together to paint the one fence is