SOLUTION: I need help with word problems. The first one is: You can paint a certain room in 5 hours. Your brother can do it in 2 hours. How long does it take the two of you working together?

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Question 344715: I need help with word problems. The first one is: You can paint a certain room in 5 hours. Your brother can do it in 2 hours. How long does it take the two of you working together?
I thought that by adding 5 and 2 and then dividing that by 2 would give me the correct amount, but this is wrong. thank you.

Found 2 solutions by nerdybill, ankor@dixie-net.com:
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
You can paint a certain room in 5 hours. Your brother can do it in 2 hours. How long does it take the two of you working together?
.
Let x = time (hours) it takes for both working together
then
x(1/5 + 1/2) = 1
Multiplying both sides by 10:
x(2 + 5) = 10
7x = 10
x = 10/7
x = 1.43 hours
or
x = 1 hour and 26 minutes

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The first one is: You can paint a certain room in 5 hours.
Your brother can do it in 2 hours. How long does it take the two of you working together?
:
This is a typical "shared work" problem and can be done this way
:
Let t = time required when working together
Let the completed job = 1
:
Each person will do a fraction of the job, the two fractions add up to 1
so we have:
+ = 1
Multiply thru by 10 to get rid of the denominators, results:
2t + 5t = 10
7t = 10
t =
t ~ 1.43 hrs or about 1 + .43(60) = 1 hr 26 min
:
:
You can confirm this on a calc
1.43/5 = .286
1.43/2 = .715
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totals: 1.000