GMAT Paper Tests
Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 3 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
A. 3.25
B. 3.6
C. 4.2
D. 4.4
E. 5.5
OA B.
Pumping alone at their respective constant rates, one inlet
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Let's assign a nice value to the volume of the tank. We want a volume that works well with the given information (1/2, 2/3, 3 hours and 6 hours).AAPL wrote:GMAT Paper Tests
Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 3 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
A. 3.25
B. 3.6
C. 4.2
D. 4.4
E. 5.5
So, let's say the tank has a total volume of 18 gallons
One inlet pipe fills an empty tank to 1/2 of capacity in 3 hours
1/2 the tank is 9 gallons.
So, this pipe fills 9 gallons in 3 hours.
So, the RATE of this pipe = 3 gallons per hour
A second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours
2/3 the tank is 12 gallons.
So, this pipe fills 12 gallons in 6 hours.
So, the RATE of this pipe = 2 gallons per hour
So, the COMBINED rate of BOTH pumps = 3 gallons per hour + 2 gallons per hour = 5 gallons per hour
How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
We need to pump 18 gallons of water, and the combined rate is 5 gallons per hour
Time = output/rate
= 18/5
= 3.6 hours
Answer: B
Cheers.
Brent
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We are given that the first inlet pipe fills an empty tank to 1/2 capacity in 3 hours. Since rate = work/time, the rate of the first inlet pipe is (1/2)/3 = 1/6.AAPL wrote:GMAT Paper Tests
Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to 1/2 of capacity in 3 hours and a second inlet pipe fills the same empty tank to 2/3 of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?
A. 3.25
B. 3.6
C. 4.2
D. 4.4
E. 5.5
OA B.
We are also given that the second inlet pipe fills the same empty tank to 2/3 capacity in 6 hours. Thus, the rate of the second inlet pipe is (2/3)/6 = 1/9.
We need to determine how many hours it will take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity.
If we let t = the time in hours the two inlet pipes are working together, then the work of the first inlet pipe = (1/6)t and the work of the second inlet pipe = (1/9)t.
Since the tank is filled, we can set total work to 1 and create the following equation:
(1/6)t + (1/9)t = 1
Multiplying the entire equation by 18, we obtain:
3t + 2t = 18
5t = 18
t = 18/5 = 3.6
Answer: B
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