Optimum Tapping

Calculus Level 3

You are filling the water into \(3\) empty inverted pyramids enclosed within a cube by opening the taps at the same time as shown above.

The tap \(A\) can release constant water rate of \(1080\) mL/min., and the tap \(C\) has constant rate of \(320\) mL/min. However, after a certain time, the pyramid below tap \(A\) will have a water height \(1\) cm. higher than the expected one while for tap \(C\), the level is \(1\) cm. lower. Only the pyramid filled with tap \(B\) has the desired volume.

At that instant, if the rate of change in height for pyramid \(A\) is \(1.5\) times higher than that of pyramid \(C\), what is the constant rate of water flow (in mL/min.) for tap \(B\)?

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