Discussion
The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
Answer: A
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ \frac{35}{b + 1} + \frac{35}{b - 1} = 12 \]
\[ \frac{35(b - 1) + 35(b + 1)}{b^{2} - 1} = \frac{70b}{b^{2} - 1} = 12 \]
\[ 70b = 12b^{2} - 12 \quad\Longrightarrow\quad 6b^{2} - 35b - 6 = 0 \]
\[ b = \frac{35 + \sqrt{1225 + 144}}{12} = \frac{35 + 37}{12} = 6 \text{ kmph} \]
Checking: 35 km at 7 kmph takes 5 hours and at 5 kmph takes 7 - twelve hours in total.
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