SOLUTION: I think i may be on the right track but not sure. Here is the problem: One hose can fill a pool in 20 hours. Another hose can fill the pool in 16 hours. How long would it take

Question 398415: I think i may be on the right track but not sure. Here is the problem: One hose can fill a pool in 20 hours. Another hose can fill the pool in 16 hours. How long would it take the two hoses, working together to fill the pool?
Here is how i set it up t/20 + t/16 with a LCD of 2. 2 x (t/20 + t/16) = 2 x 1. I reduced it down to 10t+8t=2, I combine my like terms this gives me 18t=2. Now do i divide 18 into 2 or 2 into 18? Am I on the right track to solving this problem?
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I think i may be on the right track but not sure. Here is the problem: One hose can fill a pool in 20 hours. Another hose can fill the pool in 16 hours. How long would it take the two hoses, working together to fill the pool?
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Equation:
rate + rate = together rate
1/20 + 1/16 = 1/t
Multiply thru by 80t to get:
4t + 5t = 80
9t = 80
time to fill the pool together is t = 80/9 hrs.
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Cheers,
Stan H.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
One hose can fill a pool in 20 hours. Another hose can fill the pool in 16 hours. How long would it take the two hoses, working together to fill the pool?
Here is how i set it up t/20 + t/16 with a LCD of 2. 2 x (t/20 + t/16) = 2 x 1. I reduced it down to 10t+8t=2, I combine my like terms this gives me 18t=2. Now do i divide 18 into 2 or 2 into 18? Am I on the right track to solving this problem?
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2 x (t/20 + t/16) = 2 x 1 this might work, but I don't know why you multiplied by 2
I do them like this:
The 1st hose fills 1/20 of the pool per hour
The 2nd does 1/16 per hour
Together, they do 1/20 + 1/16 = 9/80 per hour
9/80 pools per hour --> 80/9 hours per pool
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There's a shortcut, product/sum
16*20/(16+20) = 320/36 = 80/9 hours

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