Multiple choice

A boatman can row with a speed of $10$km/h in still water. The river flows at $6$km/h. If he crosses the river from one bank to other along the shortest possible path, the time taken in hours to cross the river of width $1$km is:

  1. $\dfrac{1}{8}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{1}{2}$
  4. $1$
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A Correct answer
Explanation

For the shortest path, the boat must head upstream such that its resultant velocity is perpendicular to the river flow. The resultant speed across the river is sqrt(10^2 - 6^2) = 8 km/h. Time = distance / speed = 1 / 8 hours.

AI explanation

For the shortest possible path across a flowing river, the boat must head upstream at an angle to cancel the river's drift, requiring a heading whose upstream component equals the stream speed of 6 km/h. Using the Pythagorean theorem, the actual velocity across the river is the square root of the boat's still water speed squared minus the stream speed squared, which equals sqrt((10)^2 - (6)^2) = sqrt(100 - 36) = 8 km/h. The time taken to cross the 1 km width is distance divided by this effective speed, calculated as 1/8 hours. The result is 1/8 hours.

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