Question

A crocodile at point P sees four meatballs at A, B, C, and D across the river. The crocodile moves with the same speed on land and in water. The river flows at half the crocodile’s speed. Which meatball can it catch in the shortest time?

• A. A
• B. B
• C. C
• D. D

Hint:

In river-crossing problems, the shortest time is often achieved by choosing the point closest to direct alignment, since less effort is spent countering current.

Answer 1

The Correct Option is B

Step 1: Distances.
- P is 100 m away from the near bank.
- River width = 200 m.
- Beyond river = 100 m ground.
So, total distance vertically = 400 m.
Step 2: River current effect.
Since current flows horizontally and crocodile speed is reduced diagonally, going straight across is fastest if target is aligned closer.
Step 3: Horizontal displacements.
Meatballs A, B, C, D are spaced 100 m apart along the far bank.
- A is far left,
- B is closer to alignment with P,
- C and D are far right.
Step 4: Time minimization.
Because river speed is half of crocodile’s, swimming across diagonally causes drift. The nearer the target lies to the vertical line through P, the less horizontal correction is needed. That makes B optimal. Final Answer: \[ \boxed{\text{B}} \]