SOLUTION: With both the cold and hot water faucets open, it takes 9 minutes to fulfill a bathtub. The cold water faucet alone takes 15 minutes to fill the tub. How long will it take to fill

Algebra ->  Rate-of-work-word-problems -> SOLUTION: With both the cold and hot water faucets open, it takes 9 minutes to fulfill a bathtub. The cold water faucet alone takes 15 minutes to fill the tub. How long will it take to fill       Log On


   

Question 798797: With both the cold and hot water faucets open, it takes 9 minutes to fulfill a bathtub. The cold water faucet alone takes 15 minutes to fill the tub. How long will it take to fill the tub with just the hot water faucet?
Answer by josmiceli(19441) 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%2F9+
Note that +1%2F9+ is ( 1 tub full ) / ( 9 min )
+r%5Bc%5D+=+1%2F15+
+1%2F15+%2B+r%5Bh%5D+=+1%2F9+
+r%5Bh%5D+=+1%2F9+-+1%2F15+
+r%5Bh%5D+=+5%2F45+-+3%2F45+
+r%5Bh%5D+=+2%2F45+
+r%5Bh%5D+=+1%2F22.5+
With just the hot faucet open the tub fills in 22.5 min
check:
+1%2F15+%2B+1%2F22.5+=+1%2F9+
+.0667+%2B+.0444+=+.1111+
+.1111+=+.1111+
OK