A tank is fitted with 8 pipes, some that fill the tank and others that empty the tank. Each of the fill pipes fills the tank in 8 hours, while each of the waste pipes empties it in 6 hours. lf all the pipes are kept open when the tank is full, the tank will be completely drained in 6 hours. How many of these 8 pipes are fill pipes?
Correct Answer: Description for Correct answer:
Let the number of fill pipes be 'n'. Therefore, there will be (8 - n) waste pipes.
Each fill pipe fills \( \Large \frac{1}{8} \)th of the tank in an hour. So, "n" fill pipes will fill \( \Large \frac{n}{8} \)th of the tank in an hour.
Each waste pipe drains \( \Large \frac{1}{6} \)th of the tank in a hour.
So, \"8 - n\" waste pipes will drain \( \Large \frac{8-n}{6} \)th of the tank in an hour.
Keeping these 8 pipes open results in \( \Large \frac{1}{6} \)th of the tank being drained every hour.
Hence, \( \Large \frac{n}{8}-\frac{8-n}{6}= -\frac{1}{6} \)
Solving for n, we get n = 4.
Therefore, there are 4 fill pipes and 4 waste pipes.
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