Chapter: Quadratic Equations· Mathematics Part 1 (Algebra)
Answer: Bigger tap 10 hours; smaller tap 15 hours
Let the bigger tap take \(x\) hours; the smaller takes \(x + 5\) hours.
Part filled in 1 hour: \(\dfrac{1}{x} + \dfrac{1}{x + 5} = \dfrac{1}{6}\)
\(\dfrac{2x + 5}{x(x + 5)} = \dfrac{1}{6}\)
\(6(2x + 5) = x^2 + 5x\)
\(x^2 - 7x - 30 = 0\)
\((x - 10)(x + 3) = 0\)
\(x = 10\) or \(x = -3\) (time cannot be negative).
Bigger tap: 10 hours; smaller tap: \(10 + 5 = 15\) hours.
Check: \(\dfrac{1}{10} + \dfrac{1}{15} = \dfrac{3 + 2}{30} = \dfrac{1}{6}\) ✓.