javzprobz wrote:
Working together at their constant rates, pumps X and Y can fill an empty pool to capacity in 1/3 hours. How many minutes does it take pump Y, working alone, to fill the pool?
(1) The capacity of the pool is 900 gallons.
(2) The rate of Pump X is 30 gallons per minute.
Let's see the information we have with respect to the quantities we know: Rate, Time, Work
Time taken together = 1/3 hr = 20 mins (I will prefer to work with 20 mins here because the question is asking the time in minutes and the statement 2 provides rate is mins)
We need the time taken by Y alone.
(1) The capacity of the pool is 900 gallons.
This is the capacity of the pool i.e. the work that has to be done. I can say that work done = 1 pool or I can say that work done = 900 gallons. They both represent the same thing in different units.
Now I know the work that has to be done in different units i.e. 900 gallons. From the question stem, I knew that the work to be done is 1 pool.
This means that their rate together was either 1/(1/3) = 3 pools/hr
or it can be written as 900/20 = 45 gallons/min
They both represent the same rate (of both pumps working together)
I don't know the rate of pump X so I cannot find the rate of pump Y. Not sufficient alone.
(2) The rate of Pump X is 30 gallons per minute.
Rate of pump X = 30 gallons/min but I still don't know the rate of pump Y because these units are different from the units of pool/hr that the question gives us. Since I don't know the equivalency of pool and gallons, I cannot convert one rate to another.
I don't know the combined rate in terms of gallons/min so I cannot find the rate of pump Y. Not sufficient alone.
Using both statements together,
We know that combined rate is 45 gallons/min i.e. both pumps together are putting in 45 gallons of water in one min. But pump X is putting in 30 gallons every min. So pump Y must be putting in the other 15 gallons per min.
Rate of pump Y = 15 gallons/min.
Then if I had to find the time taken by pump Y alone, I simply do
Time = work/rate = 900 gallons/15 gallons per min = 60 mins
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