SOLUTION: The cold-water faucet fills a bathtub in 12min, and the hot-water faucet fills the bathtub in 10min. If you remove the stopper, a full tub will empty in 6min. How long will it take

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Question 503644: The cold-water faucet fills a bathtub in 12min, and the hot-water faucet fills the bathtub in 10min. If you remove the stopper, a full tub will empty in 6min. How long will it take to fill the tub if both faucets are on and the stopper is removed?
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The cold-water faucet fills a bathtub in 12min, and the hot-water faucet fills the bathtub in 10min.
If you remove the stopper, a full tub will empty in 6min. How long will it take to fill the tub if both faucets are on and the stopper is removed?
:
Let t = time to fill the tub with both faucets and drain open
Let a full tub = 1
:
+ - = 1
multiply by 60, to clear the denominators
60* + 60* - 60* = 1
cancel the denominators and you have:
5t + 6t - 10t = 60
11t - 10t = 60
t = 60 minutes

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The cold-water faucet fills a bathtub in 12min, and the hot-water faucet fills the bathtub in 10min. If you remove the stopper, a full tub will empty in 6min. How long will it take to fill the tub if both faucets are on and the stopper is removed?
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Cold rate = 1/12 job/min
Warm rate = 1/10 job/min
Drain rate = 1/6 job/min
Together rate = 1/x job/min
----
Equation:
rate + rate - rate = together rate
1/12 + 1/10 - 1/6 = 1/x
Multiply thru by 60x to get:
5x + 6x - 10x = 60
x = 60 minutes (time to fill the tub together)
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Cheers,
Stan H.
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