Eugene is located at \((-12,0)\) and walking east at a rate of \(3\text{/sec}.\) Elizabeth is located at \((0,-5)\) and walking north at a rate of \(5\text{/sec}.\) What is the largest speed at which they are walking towards each other?

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Devin is pumping air into a spherical balloon. If the radius of the balloon is given by
\[ r(t) = -6 t^2 + 23t, \]
what is the time \( t \) when the volume of the balloon is maximized?

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