SOLUTION: A sink has two faucets: one for hot water and one for cold water. The sink can be filled by a cold water faucet in 3.3 minutes. if both faucets are open, the sink is filled in 2.2

Question 814638: A sink has two faucets: one for hot water and one for cold water. The sink can be filled by a cold water faucet in 3.3 minutes. if both faucets are open, the sink is filled in 2.2 minutes. how long does it take to fill the sink with just the hot-water faucet open?
Found 2 solutions by LinnW, richwmiller:
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
set c = sinks/minute from cold faucet
set h = sinks/minute from hot faucet
set t = time
t* ( c + h ) = 1 is the formula for filling 1 sink
Since it takes 2.2 minutes, this becomes
2.2 * ( c + h ) = 1
Since the cold faucet by it self fills in 3.3 minutes,
3 * ( c ) = 1
and c = 1/3
Substituting in 2.2 * ( c + h ) =1
2.2 * ( 1/3 + h ) = 1
divide each side by 2.2
1/3 + h = 1/2.2
subtract 1/3 from each side
h = 1/2.2 - 1/3
h = 0.121212
Now we have the hot rate.
So t * h = 1
t * 0.121212 = 1
t = 1/0.121212
t = 8.25

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
1/3.3+1/x=1/2.2
x = 6.6 minutes for hot water only
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