SOLUTION: Hi, can you please help me solve this word problem? Suppose one painter can paint an entire fence in 10 hours, and a second painter takes 3 hours. How many hours would it take to p

Question 1154988: Hi, can you please help me solve this word problem? Suppose one painter can paint an entire fence in 10 hours, and a second painter takes 3 hours. How many hours would it take to paint 6 fences together?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
one painter can paint an entire fence in 10 hours.
another painter can paint the an entire fence in 3 hours.
presumably all fences are the same size.
how long for both to paint 6 fences.
rate * time = quantity of work.
quantity of work is 1 fence.
first painter formula becomes rate * 10 = 1
solve for rate to get rate = 1/10.
second painter formula becomes rate * 3 = 1
solve for rate to get rate = 1/3.
when they work together their rates are additive.
1/10 + 1/3 = 3/30 + 10/30 = 13/30
their combined rate is 13/30 of a fence per hour.
when they paint 6 fences together, their combined rate is used.
the formula becomes:
13/30 * time = 6
solve for time to get:
time = 6 / (13/30) = 13.84615385 hours.
note that the first painter would take 60 hours to paint 6 fences and the second painter would take 18 hours to paint 6 fences, if each was working alone.

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