Discussion
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Answer: A
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b = \frac{(b+r) + (b-r)}{2}, \qquad r = \frac{(b+r) - (b-r)}{2} \]
\[ b = \frac{80 + 60}{2} = 70 \text{ kmph} \]
\[ r = \frac{80 - 60}{2} = 10 \text{ kmph} \]
Checking: \( 70 + 10 = 80 \) and \( 70 - 10 = 60 \). The still-water speed must lie between the two given speeds, which alone eliminates every other option.
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