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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