SOLUTION: 1. it takes one guy 5 hours to paint a house, another guy 3 hrs, and the last guy 2 hrs to paint the same house if they work together how long will it take them to paint the house

Question 404563: 1. it takes one guy 5 hours to paint a house, another guy 3 hrs, and the last guy 2 hrs to paint the same house if they work together how long will it take them to paint the house.
2. It takes 3 hours for an open valve to fill a tank and 4.5 hours for a valve to empty the tank. How long would it take to fill the tank if both valves are open.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I'll do the 1st one. The 2nd uses the same method.
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1. it takes one guy 5 hours to paint a house, another guy 3 hrs, and the last guy 2 hrs to paint the same house if they work together how long will it take them to paint the house.
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1st guy DATA:
time = 5 hrs/job ; rate = 1/5 job/hr
2nd guy DATA:
time = 3 hrs/job ; rate = 1/3 job/hr
3rd guy DATA:
time = 2 hrs/job ; rate = 1/2 job/hr
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Together data:
time = x hrs/job ; rate = 1/x job/hr
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Equation:
rate + rate + rate = together rate
1/5 + 1/3 + 1/2 = 1/x
Multiply thru by 30x to get:
6x + 10x + 15x = 30
31x = 30
x = 30/31 hrs to do the job together.
x = (30/31)(60 min) = 58.06 minutes
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Cheers,
Stan H.
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2. It takes 3 hours for an open valve to fill a tank and 4.5 hours for a valve to empty the tank. How long would it take to fill the tank if both valves are open.

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