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30 May 2023, 20:18
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D
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Difficulty:
25%
(medium)
Question Stats:
78% (02:00) correct
22%
(02:06)
wrong
based on 58
sessions
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A large water tank has an inlet pipe that can fill the tank completely in three hours, and a drain that can empty it completely in five hours. On one occasion, two hours after the filling of the tank started, the drain was accidentally opened. The error was not immediately discovered, and the drain was not closed until the tank was completely filled. Which of the following comes closest to the number of hours it took to fill the tank?
A. 3.5
B. 5.5
C. 5
D. 4.5
E. 4
A. 3.5
B. 5.5
C. 5
D. 4.5
E. 4
30 May 2023, 21:33
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This was the approach I took to solving the problem, but I got the wrong answer. I would really appreciate it if you could tell me where I went wrong.
Time taken to fill the tank = 3 hrs.
Therefore, water filled in the tank after 1hr = 1/3
Time taken to drain the tank = 5 hrs.
Water that has flown out of the tank after 1hr = 1/5.
Water in the tank after 1 hr = \(\frac{1}{3} -\frac{ 1}{5} = \frac{2}{15}\)
As the tank was filled with water in the first two hours, quantity of tank filled after 2 hrs = \(2 * \frac{1}{3} = \frac{2}{3} = \frac{10}{15}\)
Let the number of hours to fill the entire tank be x.
\(\frac{10}{15} + x(\frac{2}{15}) = \frac{15}{15}\\
\)
Solving for x, we get 2.5.
Therefore, it will take 2.5 hours to fill the entire tank.
Please help me figure out where the error in my reasoning is.
Time taken to fill the tank = 3 hrs.
Therefore, water filled in the tank after 1hr = 1/3
Time taken to drain the tank = 5 hrs.
Water that has flown out of the tank after 1hr = 1/5.
Water in the tank after 1 hr = \(\frac{1}{3} -\frac{ 1}{5} = \frac{2}{15}\)
As the tank was filled with water in the first two hours, quantity of tank filled after 2 hrs = \(2 * \frac{1}{3} = \frac{2}{3} = \frac{10}{15}\)
Let the number of hours to fill the entire tank be x.
\(\frac{10}{15} + x(\frac{2}{15}) = \frac{15}{15}\\
\)
Solving for x, we get 2.5.
Therefore, it will take 2.5 hours to fill the entire tank.
Please help me figure out where the error in my reasoning is.
30 May 2023, 23:11
Kudos
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Given: A large water tank has an inlet pipe that can fill the tank completely in three hours, and a drain that can empty it completely in five hours. On one occasion, two hours after the filling of the tank started, the drain was accidentally opened. The error was not immediately discovered, and the drain was not closed until the tank was completely filled.
Asked: Which of the following comes closest to the number of hours it took to fill the tank?
Tank filled after 2 hours of filling the tank = 2/3
Rate at which remaining tank for filled = 1/3 - 1/5 = 2/15 per hour
Time taken for remaining 1/3 tank to be filled = 1/3 * 15/2 = 5/2 = 2.5 hours
Total time taken = 2 + 2.5 = 4.5 hours
IMO D
Asked: Which of the following comes closest to the number of hours it took to fill the tank?
Tank filled after 2 hours of filling the tank = 2/3
Rate at which remaining tank for filled = 1/3 - 1/5 = 2/15 per hour
Time taken for remaining 1/3 tank to be filled = 1/3 * 15/2 = 5/2 = 2.5 hours
Total time taken = 2 + 2.5 = 4.5 hours
IMO D
