Discussion
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is
Answer: D
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ 4 \text{ h } 30 \text{ min} = 4.5 \text{ h} \]
\[ \frac{30}{15 + r} + \frac{30}{15 - r} = 4.5 \]
\[ \frac{900}{225 - r^{2}} = 4.5 \quad\Longrightarrow\quad 225 - r^{2} = 200 \]
\[ r^{2} = 25 \quad\Longrightarrow\quad r = 5 \text{ km/hr} \]
The \( r \) terms cancel when the two fractions are combined, which is what makes the quadratic so simple. Checking: 1½ hours down at 20 km/hr and 3 hours back at 10.
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