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16 Sep 2014, 01:09
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D
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Difficulty:
55%
(hard)
Question Stats:
66% (02:34) correct
34%
(02:37)
wrong
based on 349
sessions
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A filling pipe can fill an empty swimming pool in 4 hours, while a drain valve can empty the full pool in 5 hours. To fill the empty pool, the filling pipe was opened at 1:00 pm, and after some time, a drain valve was also opened. If the pool was filled at 11:00 pm, when was the drain valve opened?
A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm
A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm
16 Sep 2014, 01:09
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Official Solution:
A filling pipe can fill an empty swimming pool in 4 hours, while a drain valve can empty the full pool in 5 hours. To fill the empty pool, the filling pipe was opened at 1:00 pm, and after some time, a drain valve was also opened. If the pool was filled at 11:00 pm, when was the drain valve opened?
A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm
The rate of the filling pipe is given as \(\frac{1}{4}\) pool/hour and the rate of drain valve is given as \(\frac{1}{5}\) pool/hour. The filling pipe was opened for 10 hours, from 1:00 pm to 11:00 pm. Let x denote the time for which the drain valve was opened, then we'd have \(10*\frac{1}{4} - x*\frac{1}{5} = 1\), which gives \(x = 7.5\) hours. Hence, the drain valve was opened for 7.5 hours, and therefore was opened at 11:00 pm - 7.5 hours = 3:30 pm.
Answer: D
A filling pipe can fill an empty swimming pool in 4 hours, while a drain valve can empty the full pool in 5 hours. To fill the empty pool, the filling pipe was opened at 1:00 pm, and after some time, a drain valve was also opened. If the pool was filled at 11:00 pm, when was the drain valve opened?
A. at 2:00 pm
B. at 2:30 pm
C. at 3:00 pm
D. at 3:30 pm
E. at 4:00 pm
The rate of the filling pipe is given as \(\frac{1}{4}\) pool/hour and the rate of drain valve is given as \(\frac{1}{5}\) pool/hour. The filling pipe was opened for 10 hours, from 1:00 pm to 11:00 pm. Let x denote the time for which the drain valve was opened, then we'd have \(10*\frac{1}{4} - x*\frac{1}{5} = 1\), which gives \(x = 7.5\) hours. Hence, the drain valve was opened for 7.5 hours, and therefore was opened at 11:00 pm - 7.5 hours = 3:30 pm.
Answer: D
General Discussion
03 Jul 2023, 14:54
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
