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16 Sep 2014, 01:23
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D
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Difficulty:
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73% (02:04) correct
27%
(02:11)
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based on 368
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A drain pipe can empty a pool in 4 hours. On a rainy day, with the pool full, the drain pipe manages to empty the pool in 6 hours instead. If during the rainfall, water flows into the pool at a constant rate of 3 liters per hour, what is the capacity of the pool ?
A. \(9\) liters
B. \(18\) liters
C. \(27\) liters
D. \(36\) liters
E. \(45\) liters
A. \(9\) liters
B. \(18\) liters
C. \(27\) liters
D. \(36\) liters
E. \(45\) liters
16 Sep 2014, 01:23
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Official Solution:
A drain pipe can empty a pool in 4 hours. On a rainy day, with the pool full, the drain pipe manages to empty the pool in 6 hours instead. If during the rainfall, water flows into the pool at a constant rate of 3 liters per hour, what is the capacity of the pool ?
A. \(9\) liters
B. \(18\) liters
C. \(27\) liters
D. \(36\) liters
E. \(45\) liters
Let the rate of the draining pipe be \(x\) liters per hour. In this case, the capacity of the pool can be represented as \(C = time * rate = 4x\).
On a rainy day, the net outflow is \(x - 3\) liters per hour, and it takes 6 hours to empty the pool at this adjusted rate. Hence, the pool's capacity (C) can also be expressed as \(C = time * rate = 6(x - 3)\).
Equating the two equations, we get: \(4x = 6(x - 3)\). Solving for \(x\), we find that \(x = 9\). Consequently, the pool's capacity is \(C = 4x = 36\) liters.
Answer: D
A drain pipe can empty a pool in 4 hours. On a rainy day, with the pool full, the drain pipe manages to empty the pool in 6 hours instead. If during the rainfall, water flows into the pool at a constant rate of 3 liters per hour, what is the capacity of the pool ?
A. \(9\) liters
B. \(18\) liters
C. \(27\) liters
D. \(36\) liters
E. \(45\) liters
Let the rate of the draining pipe be \(x\) liters per hour. In this case, the capacity of the pool can be represented as \(C = time * rate = 4x\).
On a rainy day, the net outflow is \(x - 3\) liters per hour, and it takes 6 hours to empty the pool at this adjusted rate. Hence, the pool's capacity (C) can also be expressed as \(C = time * rate = 6(x - 3)\).
Equating the two equations, we get: \(4x = 6(x - 3)\). Solving for \(x\), we find that \(x = 9\). Consequently, the pool's capacity is \(C = 4x = 36\) liters.
Answer: D
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