Discussion
A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
Answer: C
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b - r = \frac{2}{1} = 2 \text{ km/h} \]
\[ b + r = \frac{1}{10/60} = 6 \text{ km/h} \]
\[ b = \frac{6 + 2}{2} = 4 \text{ km/h} \]
\[ t = \frac{5}{4} = 1.25 \text{ h} = 1 \text{ hr } 15 \text{ min} \]
"Stationary water" means no current, so the still-water speed is what applies - the 10 minutes must be converted to hours before it can be used as a speed.
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