Problem Statement
Two water taps fill a tank in $9\frac{3}{8}$ hours. The larger tap takes 10 hours less than the smaller. Find time taken by each separately.
Verified Solution & Marking Scheme
Rates Equation
$\frac{1}{x} + \frac{1}{x - 10} = \frac{8}{75}$
Form Quadratic
$75(2x - 10) = 8(x^2 - 10x) \implies 4x^2 - 115x + 375 = 0$
Factorize
$(x - 25)(4x - 15) = 0 \implies x = 25 \text{ hours}$. Larger tap takes $15$ hours.