Discussion
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Answer: C
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ 8 \text{ h } 48 \text{ min} = 8.8 \text{ h} \]
Speeds are inversely proportional to times over the same distance:
\[ \frac{b + r}{b - r} = \frac{8.8}{4} = \frac{11}{5} \]
\[ 5(b + r) = 11(b - r) \quad\Longrightarrow\quad 16r = 6b \]
\[ \frac{b}{r} = \frac{8}{3} \quad\Longrightarrow\quad 8 : 3 \]
The distance cancels, so "cannot be determined" is wrong - a ratio of times is enough to fix a ratio of speeds.
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