SOLUTION: "3 Pipes of different sizes are filling up a pool. Pipe1 fills it up a third of the time that it takes Pipe3, and Pipe2 fills it up a half of the time that it takes Pipe3. How long

Question 71096: "3 Pipes of different sizes are filling up a pool. Pipe1 fills it up a third of the time that it takes Pipe3, and Pipe2 fills it up a half of the time that it takes Pipe3. How long will it take each pipe to fill up the pool by itself?"
-if you set up a table, i'm not sure where the variable would go, or when you set up the equation[[Pipe 1 work done + Pipe 2 work done + Pipe 3 work done = ?]] should that ? be a 1, for one hour, or a 3, for the 3 hours it took to fill up the pool with all of the pipes?
Found 2 solutions by stanbon, jorel1380:
Answer by stanbon(57224) (Show Source):
You can put this solution on YOUR website!
"3 Pipes of different sizes are filling up a pool. Pipe 1 fills it up a third of the time that it takes Pipe 3, and Pipe 2 fills it up a half of the time that it takes Pipe3. How long will it take each pipe to fill up the pool by itself?"
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Let time for Pipe 3 be 6x hrs/job ; Rate = 1/6x job/hr
Pipe 2 time is 3x hrs/job ; Rate = 1/3x job/hr
Pipe 1 time is 2x hrs/job ; Rate = 1/2x job/hr
Time for all to fill = 3 hrs/job ; Rate = 1/3 job/hr
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EQUATION:
rate + rate + rate = rate together
1/6x + 1/3x + 1/2x = 1/3
Multiply thru by 6x to get:
1 + 2 + 3 = 2x
x=3 hrs.
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Pipe 3 takes 6x or 18 hrs alone
Pipe 2 takes 3x or 9 hrs. alone
Pipe 1 takes 2x or 6 hrs. alone
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Cheers,
Stan H.

Answer by jorel1380(2518) (Show Source):
You can put this solution on YOUR website!
It doesn't necessarily take three hours for all three pipes to fill the pool. To solve this problem, let's take pipe 3 as our starting point. To fill the pool, pipe 3 working alone would take 1/x time. Since pipe 1 takes 1/3rd the time, it would be represented by 1/1x/3. Likewise, pipe 2 would be 1/1x/2. To fill one pool our equation would be: 1/x + 2/x + 3/x = 1 whole pool. X(1/x + 2/x + 3/x) = (1)X. 1 + 2 + 3 = X, or X = 6 hours for one whole pool. The other times are 1/2 * 6, or 3 hours, and 1/3 * 6, or 2 hours to fill a pool. Checking: 1/2 + 1/3 + 1/6 = 1.