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09 Jul 2024, 07:00
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Difficulty:
95%
(hard)
Question Stats:
50% (02:17) correct
50%
(02:30)
wrong
based on 624
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On Monday, a pipe working continuously filled an empty tank at an average (arithmetic mean) rate of 75 liters per hour. The next day, the pipe began filling another empty tank of the same volume. However, during this process, it was turned off for some time due to maintenance, resulting in a longer filling time. This reduced its average filling rate to 60 liters per hour. How many minutes per hour was the pipe turned off on Tuesday?
A. 10
B. 12
C. 15
D. 20
E. 25
A. 10
B. 12
C. 15
D. 20
E. 25
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09 Jul 2024, 08:00
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Official Solution:
On Monday, a pipe working continuously filled an empty tank at an average (arithmetic mean) rate of 75 liters per hour. The next day, the pipe began filling another empty tank of the same volume. However, during this process, it was turned off for some time due to maintenance, resulting in a longer filling time. This reduced its average filling rate to 60 liters per hour. How many minutes per hour was the pipe turned off on Tuesday?
A. 10
B. 12
C. 15
D. 20
E. 25
There are many ways to solve this question; however, arguably the least error-prone method is to assume a specific volume for the tank. Let's say its volume is 300 liters (the least common multiple of 75 and 60). This would mean that without the maintenance interruption, the pipe would take \(\frac{300}{75} = 4\) hours to fill the tank. With the maintenance interruption, it would take \(\frac{300}{60} = 5\) hours. Thus, the pipe was turned off for 1 hour out of 5, which makes 1/5 of an hour per hour, or 12 minutes per hour.
Answer: B
On Monday, a pipe working continuously filled an empty tank at an average (arithmetic mean) rate of 75 liters per hour. The next day, the pipe began filling another empty tank of the same volume. However, during this process, it was turned off for some time due to maintenance, resulting in a longer filling time. This reduced its average filling rate to 60 liters per hour. How many minutes per hour was the pipe turned off on Tuesday?
A. 10
B. 12
C. 15
D. 20
E. 25
There are many ways to solve this question; however, arguably the least error-prone method is to assume a specific volume for the tank. Let's say its volume is 300 liters (the least common multiple of 75 and 60). This would mean that without the maintenance interruption, the pipe would take \(\frac{300}{75} = 4\) hours to fill the tank. With the maintenance interruption, it would take \(\frac{300}{60} = 5\) hours. Thus, the pipe was turned off for 1 hour out of 5, which makes 1/5 of an hour per hour, or 12 minutes per hour.
Answer: B
General Discussion
09 Jul 2024, 07:15
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How many minutes per hour was the pipe turned off on Tuesday?
Rate Pipe No. 1 = 75 Lt/hr
Rate Pipe No. 2 = 60 Lt/hr
Analyzing at what time both filled same amount of water:
75 (1) = 75
75 (2) = 150
75 (3) = 225
75 (4) = 300
60 (1) = 60
60 (2) = 120
60 (3) = 180
60 (4) = 240
60 (5) = 300
So, difference between both rates is 1 hour. So, divide 60 Minutes (difference) / total time=
=60/5 = 12 minutes off per hour.
Answer: B. 12
Rate Pipe No. 1 = 75 Lt/hr
Rate Pipe No. 2 = 60 Lt/hr
Analyzing at what time both filled same amount of water:
75 (1) = 75
75 (2) = 150
75 (3) = 225
75 (4) = 300
60 (1) = 60
60 (2) = 120
60 (3) = 180
60 (4) = 240
60 (5) = 300
So, difference between both rates is 1 hour. So, divide 60 Minutes (difference) / total time=
=60/5 = 12 minutes off per hour.
Answer: B. 12
