SOLUTION: With both the cold water and hot water faucets​ open, it takes 7 minutes to fill a bathtub. The cold water faucet alone takes 9 minutes to fill the tub. How long will it take to

Algebra ->  Rate-of-work-word-problems -> SOLUTION: With both the cold water and hot water faucets​ open, it takes 7 minutes to fill a bathtub. The cold water faucet alone takes 9 minutes to fill the tub. How long will it take to       Log On


   

Question 1155962: With both the cold water and hot water faucets​ open, it takes 7 minutes to fill a bathtub. The cold water faucet alone takes 9 minutes to fill the tub. How long will it take to fill the tub with just the hot water​ faucet?
Found 4 solutions by josgarithmetic, MathLover1, MathTherapy, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
h, time for the HOT water faucet to fill tub

1%2F9%2B1%2Fh=1%2F7
-
63h%281%2F9%2B1%2Fh%29=63h%2F7
7h%2B63=9h
63=2h
highlight%28h=31%261%2F2%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!



Let +r%5Bc%5D+ = the rate of filling with cold water faucet alone
Let +r%5Bh%5D+ = the rate of filling with hot water faucet alone
+r%5Bc%5D+%2B+r%5Bh%5D+=+1%2F7+
Note that +1%2F7+ is ( 1 tub full ) / ( 7 min )
+r%5Bc%5D+=+1%2F9
+1%2F9+%2B+r%5Bh%5D+=+1%2F7+
+r%5Bh%5D+=+1%2F7+-+1%2F9+
+r%5Bh%5D+=+9%2F63+-+7%2F63+
+r%5Bh%5D+=+2%2F63+
+r%5Bh%5D+=+1%2F31.5+
With just the hot faucet open the tub fills in highlight%2831.5%29 min
check:
+1%2F9+%2B+1%2F31.5+=+1%2F7+
+0.14285714285714285+=+0.14285714285714285+
+0.143+=+0.143+

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

With both the cold water and hot water faucets​ open, it takes 7 minutes to fill a bathtub. The cold water faucet alone takes 9 minutes to fill the tub. How long will it take to fill the tub with just the hot water​ faucet?
Let time hot water faucet takes be H

Then hot water faucet does 1%2FH of job in 1 minute

Cold water faucet takes 9 hours, and can do 1%2F9 of work in 1 minute

We then get: matrix%281%2C3%2C+1%2FH+%2B+1%2F9%2C+%22=%22%2C+1%2F7%29

63 + 7H = 9H ------- Multiplying by LCD, 63H

63 = 2H

H, or time hot water faucet takes =

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


All three solutions you have received so far use some variation of the same algebraic method. Here is an alternative method that I find many students prefer.

Consider the least common multiple (LCM) of the two given times, which is 63 minutes.

With both faucets working, being able to fill the tub together in 7 minutes, in 63 minutes they could fill the tub 63/7 = 9 times.

With only the cold water faucet working, being able to fill the tub alone in 9 minutes, in 63 minutes it could fill the tub 63/9 = 7 times.

That means in 63 minutes the hot water faucet alone could fill the tub 9-7 = 2 times; that means the time it would take the hot water faucet alone to fill the tub (once) would be 63/2 = 31.5 minutes.