# Tap A and B

Taps $$A$$ and $$B$$ together can fill a bucket in 6 minutes. Their rates (in which they each can fill the bucket) are different and accelerate as follows:

• Tap A alone can fill the bucket in 8 minutes with initial speed $$\SI[per-mode=symbol]{2}{\milli\liter\per\second}$$ and acceleration $$\SI[per-mode=symbol]{2}{\milli\liter\per\second\squared}.$$
• Tap B alone can fill the bucket in $$x$$ minutes with initial speed $$\SI[per-mode=symbol]{3}{\milli\liter\per\second}$$ and acceleration $$\SI[per-mode=symbol]{n}{\milli\liter\per\second\squared}$$.

Find $$n$$ to two decimal places.

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