Discussion
The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. The speed of the stream is?
Answer: A
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ \frac{30}{15 - r} + \frac{30}{15 + r} = 4.5 \]
Over the common denominator \( 225 - r^{2} \):
\[ \frac{30(15 + r) + 30(15 - r)}{225 - r^{2}} = \frac{900}{225 - r^{2}} = 4.5 \]
\[ 225 - r^{2} = 200 \quad\Longrightarrow\quad r^{2} = 25 \quad\Longrightarrow\quad r = 5 \text{ km/hr} \]
The \( r \) terms cancel in the numerator, leaving a simple equation. Checking: 30 km at 10 km/hr takes 3 hours and at 20 km/hr takes 1½.
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