Discussion
An ocean current flows at a rate of 1.5 km/hr. A shark can swim in still water at the rate 4.5 km/hr. What is the average speed for the entire distance travelled, if the shark swims from India to Australia and comes back?
Answer: B
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = 6 \text{ km/h}, \qquad b - r = 3 \text{ km/h} \]
Average speed over a round trip is total distance over total time, which gives the harmonic mean, not the arithmetic one:
\[ \bar{v} = \frac{2 \times 6 \times 3}{6 + 3} = \frac{36}{9} = 4 \text{ km/h} \]
The arithmetic mean of 6 and 3 is 4.5, which is too high: more time is spent at the slower speed, so the slow leg carries more weight. Notice the answer is below the shark's still-water speed of 4.5 - a current always costs time on a round trip.
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