Discussion

A boat goes 100 km downstream in 10 hours and 75 km upstream in 15 hours. The speed of the stream is?

Answer: D

Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then

\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]

\[ b + r = \frac{100}{10} = 10 \text{ km/h}, \qquad b - r = \frac{75}{15} = 5 \text{ km/h} \]

\[ r = \frac{10 - 5}{2} = 2.5 = 2\tfrac{1}{2} \text{ km/h} \]

The stream's speed is half the difference of the two speeds, not the difference itself - the 5 km/h option is exactly that omission.

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