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29 Jul 2024, 02:09
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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
29 Jul 2024, 02:09
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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
29 Aug 2024, 09:43
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Bunuel
Does On Monday, a pipe working continuously mean that the pipe worked during the whole 24 hours throughout Monday? If yes, then it seems we easily can get the volume of the tank by multiplying 75 liters per hour by 24 hours = 1800 liter is the tank capacity?
Is my approach regarding the tank capacity correct?
Thanks in advance!
Does On Monday, a pipe working continuously mean that the pipe worked during the whole 24 hours throughout Monday? If yes, then it seems we easily can get the volume of the tank by multiplying 75 liters per hour by 24 hours = 1800 liter is the tank capacity?
Is my approach regarding the tank capacity correct?
Thanks in advance!
