Discussion
What will be the boat's speed in still water and speed of river, if the boat takes 12 hours to row 48 km upstream and 8 hours to row the same distance downstream?
Answer: C
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b - r = \frac{48}{12} = 4 \text{ km/h}, \qquad b + r = \frac{48}{8} = 6 \text{ km/h} \]
\[ b = \frac{6 + 4}{2} = 5 \text{ km/h}, \qquad r = \frac{6 - 4}{2} = 1 \text{ km/h} \]
Half the sum gives the boat and half the difference gives the river - the standard pair of formulas, and the reason the longer time always belongs to the upstream leg.
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