SOLUTION: It takes the hot water faucet 4 times as long to fill a bathtub as it does the cold water faucet. Left on together, the cold and hot water faucets take 3 minutes to fill the tub. H

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes the hot water faucet 4 times as long to fill a bathtub as it does the cold water faucet. Left on together, the cold and hot water faucets take 3 minutes to fill the tub. H      Log On


   

Question 1129099: It takes the hot water faucet 4 times as long to fill a bathtub as it does the cold water faucet. Left on together, the cold and hot water faucets take 3 minutes to fill the tub. How long will it take the cold water faucet to fill the tub by itself?
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
x, minutes for cold water faucet to fill tub
4x, minutes for hot water faucet to fill tub

1%2Fx%2B1%2F%284x%29=1%2F3
-
12x%281%2Fx%2B1%2F%284x%29%29=12%281%2F3%29x
12%2B3=4x
15=4x
x=15%2F4
highlight%28x=3%263%2F4%29



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check:
1%2F%2815%2F4%29%2B1%2F%284%2815%2F4%29%29
4%2F15%2B1%2F15
5%2F15
1%2F3

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


A solution using logical reasoning instead of formal algebra....

The hot water faucet takes 4 times as long as the cold water faucet to fill the tub.

That means that in filling the tub together in 3 minutes, the cold water faucet fills 4/5 of the tub.

So to fill the whole tub by itself the cold water faucet has to work 5/4 as long; 3 minutes times 5/4 is 15/4 minutes, or 3 minutes 45 seconds.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
From the condition, the cold water facet is 4 times as productive as the hot water facet.


So, when both facets are turned on, it is equivalent as if 5 hot water facet are turned on (from the inflow rate point of view).


Thus, 5 hot water facets will fill the bathtub in 3 minutes - hence, one hot water facet will fill it in 15 minutes.


It implies, that cold water facet will fill the bathtub in 4 times faster, i.e. in  15%2F4 minutes = 33%2F4 minutes = 3 minutes and 45 seconds.