SOLUTION: A tub can be filled in 6min if both the hot and cold faucets are turned on. If the tub can be filled in 10 min with cold water, how long would it take to fill that tub with hot wat

Question 903957: A tub can be filled in 6min if both the hot and cold faucets are turned on. If the tub can be filled in 10 min with cold water, how long would it take to fill that tub with hot water?
Found 2 solutions by Theo, richwmiller:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let C = rate of cold water filling the tub.
let H = rate of hot water filling the tub.
together, the rates are additive so you get (H+C) * 6 = 1
that's rate * time = quantity.
rate is H + C
time is 6 minutes
quantity is 1 full tub

you know that (H+C)*T = 1
H = rate of hot water
C = rate of cold water
T = time in minutes

you also know that C*10 = 1
solve for C and you get C = 1/10

replace C with 1/10 in (H+C)*T = 1 and you get (H+1/10)*6 = 1
simplify to get 6H + 6/10 = 1
subtract 6/10 from both sides of the equation to get 6H = 4/10
divide both sides of the equation by 6 to get H = 4/60 = 1/15.

the rate of the cold water is 1/10 of a full tub in 1 minute.
the rate of the hot water is 1/15 of a full tub in 1 minute.

the hot water alone will fill the tub using the equation of HT = 1
replace H with 1/15 and you get 1/15*T = 1
solve for T and you get T = 15 minutes.

the cold water can fill the tub in 10 minutes.
the hot water can fill the tub in 15 minutes.
when the cold water and the hot water are both turned on, they can fill the tub in 6 minutes.

(H+C)*6 = 1 becomes (1/15 + 1/10)*6 = 1 which becomes (2/30 + 3/30)*6 = 1 which becomes 5/30*6 = 1 which becomes 1 = 1, confirming the solution is good.

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
rate for A alone 10
rate for A & B together 6
1/a+1/b=1/x
1/10+1/b=1/6
1/b=1/6-1/10
1/b=10/60-6/60
1/b=4/60
1/b=1/15
b=15
rate for B alone 15
check
1/10+1/15=1/6
15/150+10/150=1/6
25/150=1/6
ok

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