A tank is connected to 10 pipes that are either inlet or outlet types.

A tank is connected to 10 pipes that are either inlet or outlet types. Each inlet pipe can fill an empty tank in 8 hours, and each outlet pipe can empty a full tank in 6 hours. If all pipes are open, the tank fills in 12 hours. How many of the pipes are inlets?

A. 4
B. 5
C. 6
D. 7
E. 8


Let's assume there are \(x\) inlet and \(y\) outlet pipes.

Since each inlet pipe can fill an empty tank in 8 hours, then the rate of one inlet pipe is \(\frac{1}{8}\) tank/hour, and consequently, the rate of \(x\) inlet pipes is \(\frac{x}{8}\) tank/hour.

Similarly, since each outlet pipe can empty a full tank in 6 hours, then the rate of one outlet pipe is \(\frac{1}{6}\) tank/hour, and consequently, the rate of \(y\) outlet pipes is \(\frac{y}{6}\) tank/hour.

Next, since with all pipes open, the tank fills in 12 hours, we have \(\frac{x}{8} - \frac{y}{6} = \frac{1}{12}\).

We also know that there are a total of 10 pipes, so \(x + y = 10\). Substituting \(y = 10 - x\) in the above equation, we get:

\(\frac{x}{8} - \frac{10-x}{6} = \frac{1}{12}\)

Multiply by the LCM of 8, 6, and 12, which is 24, to eliminate the fractions:

\(3x - 4(10-x)=2\)

\(x = 6\)

Therefore, there are 6 inlet pipes.


Answer: C