# 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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