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16 Sep 2014, 00:24
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
65% (02:33) correct
35%
(02:49)
wrong
based on 669
sessions
History
Date
Time
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Not Attempted Yet
Samson can fill an empty bathtub with a cold water tap in 6 minutes and 40 seconds or with a hot water tap in 8 minutes. Draining the full bathtub, while the plug is out, takes 13 minutes and 20 seconds. How long will it take Samson to fill the empty bathtub completely with both the cold and hot taps running, while the plug is out?
A. 16 minutes
B. 12 minutes
C. 8.6 minutes
D. 5 minutes
E. 4.75 minutes
A. 16 minutes
B. 12 minutes
C. 8.6 minutes
D. 5 minutes
E. 4.75 minutes
16 Sep 2014, 00:24
Kudos
Bookmarks
Official Solution:
Samson can fill an empty bathtub with a cold water tap in 6 minutes and 40 seconds or with a hot water tap in 8 minutes. Draining the full bathtub, while the plug is out, takes 13 minutes and 20 seconds. How long will it take Samson to fill the empty bathtub completely with both the cold and hot taps running, while the plug is out?
A. 16 minutes
B. 12 minutes
C. 8.6 minutes
D. 5 minutes
E. 4.75 minutes
The cold water tap can fill the bathtub in \(6\frac{2}{3}=\frac{20}{3}\) minutes, giving a rate of \(\frac{3}{20}\) tubs per minute. Similarly, the hot water tap can fill the bathtub in 8 minutes, giving a rate of \(\frac{1}{8}\) tubs per minute. On the other hand, draining the bathtub takes \(13\frac{1}{3}=\frac{40}{3}\) minutes, giving a rate of \(\frac{3}{40}\) tubs per minute.
Therefore, the net inflow rate when both the cold and hot water taps are running and the drain is open is given by \(\frac{3}{20} + \frac{1}{8}-\frac{3}{40}=\frac{6}{40} + \frac{5}{40}-\frac{3}{40}=\frac{8}{40}=\frac{1}{5}\) tubs per minute.
Since the rate is the reciprocal of time, the time it will take to fill the bathtub completely is therefore 5 minutes.
Answer: D
Samson can fill an empty bathtub with a cold water tap in 6 minutes and 40 seconds or with a hot water tap in 8 minutes. Draining the full bathtub, while the plug is out, takes 13 minutes and 20 seconds. How long will it take Samson to fill the empty bathtub completely with both the cold and hot taps running, while the plug is out?
A. 16 minutes
B. 12 minutes
C. 8.6 minutes
D. 5 minutes
E. 4.75 minutes
The cold water tap can fill the bathtub in \(6\frac{2}{3}=\frac{20}{3}\) minutes, giving a rate of \(\frac{3}{20}\) tubs per minute. Similarly, the hot water tap can fill the bathtub in 8 minutes, giving a rate of \(\frac{1}{8}\) tubs per minute. On the other hand, draining the bathtub takes \(13\frac{1}{3}=\frac{40}{3}\) minutes, giving a rate of \(\frac{3}{40}\) tubs per minute.
Therefore, the net inflow rate when both the cold and hot water taps are running and the drain is open is given by \(\frac{3}{20} + \frac{1}{8}-\frac{3}{40}=\frac{6}{40} + \frac{5}{40}-\frac{3}{40}=\frac{8}{40}=\frac{1}{5}\) tubs per minute.
Since the rate is the reciprocal of time, the time it will take to fill the bathtub completely is therefore 5 minutes.
Answer: D
General Discussion
13 Mar 2023, 02:33
Kudos
Bookmarks
is it possible/ wise to approach this problem by approximation?
rate of H plus rate of C = ~7/25
rate of Drain =~ 1/13
7/25 - 1/13 =~ 5/25 = 1/5.
rate of H plus rate of C = ~7/25
rate of Drain =~ 1/13
7/25 - 1/13 =~ 5/25 = 1/5.
