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16 Sep 2014, 00:46
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If both valves are open simultaneously, they can fill an empty pool in 48 minutes. The first valve, when working independently, takes 2 hours to fill the pool. If the second valve releases 50 cubic meters of water more than the first valve every minute, what is the capacity of the pool?
A. 9,000 cubic meters
B. 10,500 cubic meters
C. 11,750 cubic meters
D. 12,000 cubic meters
E. 12,500 cubic meters
A. 9,000 cubic meters
B. 10,500 cubic meters
C. 11,750 cubic meters
D. 12,000 cubic meters
E. 12,500 cubic meters
16 Sep 2014, 00:46
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Official Solution:
If both valves are open simultaneously, they can fill an empty pool in 48 minutes. The first valve, when working independently, takes 2 hours to fill the pool. If the second valve releases 50 cubic meters of water more than the first valve every minute, what is the capacity of the pool?
A. 9,000 cubic meters
B. 10,500 cubic meters
C. 11,750 cubic meters
D. 12,000 cubic meters
E. 12,500 cubic meters
Let the rate of the first valve be \(x\) cubic meters per minute. The rate of the second valve will then be \(x + 50\) cubic meters per minute.
Given that both valves together fill the pool in 48 minutes, the capacity of the pool can be calculated as \(C = \text{time}*\text{combined rate} = 48 \times (x + x + 50) = 48(2x + 50)\).
Since the first valve alone fills the pool in 2 hours (or 120 minutes), the capacity of the pool can also be represented as \(C = \text{time} *\text{rate} = 120x\).
Equating the two expressions for \(C\), we have \(120x = 48(2x + 50)\). Solving for \(x\), we get \(x = 100\), which implies \(C = 120x = 12,000\) cubic meters.
Answer: D
If both valves are open simultaneously, they can fill an empty pool in 48 minutes. The first valve, when working independently, takes 2 hours to fill the pool. If the second valve releases 50 cubic meters of water more than the first valve every minute, what is the capacity of the pool?
A. 9,000 cubic meters
B. 10,500 cubic meters
C. 11,750 cubic meters
D. 12,000 cubic meters
E. 12,500 cubic meters
Let the rate of the first valve be \(x\) cubic meters per minute. The rate of the second valve will then be \(x + 50\) cubic meters per minute.
Given that both valves together fill the pool in 48 minutes, the capacity of the pool can be calculated as \(C = \text{time}*\text{combined rate} = 48 \times (x + x + 50) = 48(2x + 50)\).
Since the first valve alone fills the pool in 2 hours (or 120 minutes), the capacity of the pool can also be represented as \(C = \text{time} *\text{rate} = 120x\).
Equating the two expressions for \(C\), we have \(120x = 48(2x + 50)\). Solving for \(x\), we get \(x = 100\), which implies \(C = 120x = 12,000\) cubic meters.
Answer: D
General Discussion
20 Dec 2014, 09:51
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I had a different approach, which is more lengthy, since I could not even consider the method used above 
rate of pump A = 1/120 (2h = 120 min)
rate A+B = 1/48
Rate B = 1/48 - 1/120 = 1/80
1/80 - 1/120 is 50m^3
1/240 = 50m^3
1 pool = 50m^3 * 240 = 12,000
i am not sure whether this is a correct method
rate of pump A = 1/120 (2h = 120 min)
rate A+B = 1/48
Rate B = 1/48 - 1/120 = 1/80
1/80 - 1/120 is 50m^3
1/240 = 50m^3
1 pool = 50m^3 * 240 = 12,000
i am not sure whether this is a correct method
