Answer: Larger tap 3 hours, smaller tap 6 hours
Let the larger tap take \(x\) hours; the smaller takes \(x + 3\) hours.
\[\frac{1}{x} + \frac{1}{x + 3} = \frac{1}{2}\]\[2(2x + 3) = x(x + 3)\]\[x^2 - x - 6 = 0\]\[(x - 3)(x + 2) = 0\]\(x = 3\). Check: \(\frac{1}{3} + \frac{1}{6} = \frac{1}{2}\).