Discussion
It takes P 1 hour to row to a place and to come back. If the river is running at 2.4 km/hr and P has a speed of 12 km/hr in still water, what distance is the place from P’s starting point?
Answer: D
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = 14.4 \text{ km/h}, \qquad b - r = 9.6 \text{ km/h} \]
The round trip to a place \( D \) away takes 1 hour:
\[ \frac{D}{14.4} + \frac{D}{9.6} = 1 \]
\[ D\left(\frac{1}{14.4} + \frac{1}{9.6}\right) = D\left(\frac{2 + 3}{28.8}\right) = 1 \]
\[ \frac{5D}{28.8} = 1 \quad\Longrightarrow\quad D = 5.76 \text{ km} \]
The 4.8 km on offer is what you get by using the still-water speed of 12 km/h for both legs - but the current does not cancel out over a round trip.
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