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Question 1189434: Brooke’s empty tub fills in 20 mins with the drain plugged, and her full tub drains in 10 mins with the water off. How many minutes would it take the full tub to drain while the water is on?
Found 3 solutions by math_tutor2020, greenestamps, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
The LCM of 20 and 10 is 20. This LCM value will be used for the capacity of the tub (though you can use any multiple of this).
Consider the tub's capacity is 20 gallons.
If it fills in 20 minutes, with the drain plugged, then the faucet's unit rate is
(20 gallons)/(20 minutes) = 1 gallon per minute
If the full tub empties in 10 minutes, without the faucet going, then the unit rate here is:
(20 gallons)/(10 minutes) = 2 gallons per minute
I will subtract the two unit rates since they work against one another.
overall rate = fill rate - drain rate = (1 gal/min) - (2 gal/min) = -1 gal/min
The negative result means we're losing water more than gaining it.
The drain is winning the battle. This fits with the fact that the drain is able to get the job done faster compared to the faucet.
With the faucet on and the drain open, the drain will empty the tub faster than the faucet can fill it up.
At some point, the tub will be empty.
Specifically, that would be 20 minutes into the scenario. This is because
(-1 gal/min)*(20 min) = -20 gallons
Answer: 20 minutes
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The solution from the other tutor is fine, but it seems like a lot of work....
Using the standard method for solving a problem like this -- by looking at the fractions of the "job" each "worker" does in 1 minutes -- is much easier.
In 1 minute, the faucet fills 1/20 of the tub; in 1 minute the drain empties 1/10 of the tub.
So in 1 minute the fraction of the tub that is emptied is 1/10-1/20 = 1/20.
Therefore it will take 20 minutes for the whole tub to empty.
ANSWER: 20 minutes
Answer by ikleyn(52806)  (Show Source):
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