Problem Statement
A motor boat whose speed is $18\text{ km/h}$ in still water takes 1 hour more to go $24\text{ km}$ upstream than to return downstream to the same spot. Find the speed of the stream.
Verified Solution & Marking Scheme
Set Up Time Equation
Let stream speed be $x$. Upstream time = $\frac{24}{18 - x}$, Downstream time = $\frac{24}{18 + x}$.
Clear Fractions
$\frac{24}{18 - x} - \frac{24}{18 + x} = 1 \implies 24\left(\frac{2x}{324 - x^2}\right) = 1 \implies x^2 + 48x - 324 = 0$
Factorize Quadratic
$(x + 54)(x - 6) = 0 \implies x = 6 \text{ km/h (since } x > 0)$.