SOLUTION: Left on together, the cold and hot water faucets of a certain bathtub take 6minutes to fill the tub. If it takes the cold water faucet 14 minutes to fill the tub by itself, how lon
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-> SOLUTION: Left on together, the cold and hot water faucets of a certain bathtub take 6minutes to fill the tub. If it takes the cold water faucet 14 minutes to fill the tub by itself, how lon
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Question 1146364: Left on together, the cold and hot water faucets of a certain bathtub take 6minutes to fill the tub. If it takes the cold water faucet 14 minutes to fill the tub by itself, how long will it take the hot water faucet to fill the tub in it’s own?
No rounding needed Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! rate * time = quantity of work completed.
h = rate of hot water.
c = rate of cold water.
quantity of work completed is 1 full tub.
when they work together, the rate becomes (c + h) and formula becomes 6 * (c + h) = 1
when only the cold water is running, the formula becomes 14 * c = 1
you have two equations that need to be solved simultaneously.
they are:
6 * (c + h) = 1
14 * c = 1
simplify the first equation and leave the second equation as is to get:
6 * c + 6 * h = 1
14 * c = 1
multiply both sides of the first equation by 14 and multiply both sides of the second equation by 6 to get:
84 * c + 84 * h = 14
84 * c = 6
subtract the second equation from the first to get:
84 * h = 8
solve for h to get:
h = 8/84 = 2/21
from 14c = 1, solve for c to get c = 1/14
6 * (h + c) = 1 becomes 6 * h + 6 * c = 1 which becomes 6 * 1/14 + 6 * 2/21 = 1.
simplify to get 6/14 + 12/21 = 1
place both fractions under the common denominator of 42 to get:
18/42 + 24/42 = 1
combine like terms to get 42/42 = 1
simplify to get 1 = 1
this confirms the solution is correct.
the rate of the cold water is 1/14 of the tub in 1 minute.
the rate of the hot water is 2/21 of the tub in 1 minute.
the formula when they work together is (1/14 + 2/21) * T = 1
solve for T to get T = 1 / (1/14 + 2/21) = 1 / (3/42 + 4/21) = 1 / (7/42) = 1 * 42 / 7 = 1 * 6 = 6 minutes.
this agrees with the problem statement that says it takes 6 minutes to fill the tub when they are working together.
when the hot water alone is working, the formula becomes 2/21 * T = 1
solve for T to get T = 1 / (2/21) = 1 * 21 / 2 = 10.5 minutes.
You can put this solution on YOUR website! Left on together, the cold and hot water faucets of a certain bathtub take 6minutes to fill the tub. If it takes the cold water faucet 14 minutes to fill the tub by itself, how long will it take the hot water faucet to fill the tub in it’s own?
No rounding needed
Let amount of time hot water faucet takes, be H
Then the hot and cold water faucets can fill in 1 minute
We then get:
42 + 3H = 7H ------- Multiplying by LCD, 42H
42 = 4H
H, or amount of time hot water faucet takes, by itself, to fill tub =
