Discussion
The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Answer: C
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ \frac{6}{b + 4} + \frac{6}{b - 4} = 2 \]
Over the common denominator \( b^{2} - 16 \):
\[ \frac{6(b - 4) + 6(b + 4)}{b^{2} - 16} = \frac{12b}{b^{2} - 16} = 2 \]
\[ 12b = 2b^{2} - 32 \quad\Longrightarrow\quad b^{2} - 6b - 16 = 0 \]
\[ (b - 8)(b + 2) = 0 \quad\Longrightarrow\quad b = 8 \text{ kmph} \]
The negative root is discarded. Checking: 6 km at 12 kmph takes half an hour and 6 km at 4 kmph takes one and a half - two hours in total.
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