Two fisherman A and B decide to have an unusual race. Each has an engine powdered boat that travels at 10 m/s in still water . A will go to point directly across the starting point and return. B will travel 100 m downstream and then return. Who wins and what is the time of return?

To determine who wins the race between fishermen A and B, we need to analyze their respective journeys carefully. Both have boats that can travel at a speed of 10 m/s in still water, but their paths differ significantly. Let's break down the problem step by step.

Fisherman A's Journey

Fisherman A travels directly across the river and back. Assuming the river has a width of d meters, the total distance A covers is:

• Across the river: d meters
• Back: d meters

The total distance for A is 2d meters. Since A's speed is 10 m/s, the time taken for A to complete the journey can be calculated using the formula:

Time = Distance / Speed

Thus, the time for A is:

Time_A = 2d / 10 = d / 5 seconds.

Fisherman B's Journey

Fisherman B travels 100 meters downstream and then returns. The total distance B covers is:

• Downstream: 100 meters
• Back upstream: 100 meters

The total distance for B is 200 meters. However, we must consider the effect of the river's current on B's speed. Let's denote the speed of the current as v_c m/s. When B travels downstream, his effective speed is:

Speed_downstream = 10 + v_c

When B returns upstream, his effective speed is:

Speed_upstream = 10 - v_c

Now, we can calculate the time taken for each leg of B's journey:

• Time downstream: Time_downstream = 100 / (10 + v_c)
• Time upstream: Time_upstream = 100 / (10 - v_c)

The total time for B is:

Time_B = Time_downstream + Time_upstream

Time_B = 100 / (10 + v_c) + 100 / (10 - v_c)

Comparing Times

To find out who wins, we need to compare Time_A and Time_B. The winner will be the one with the lesser time. However, we need to know the width of the river (d) and the speed of the current (v_c) to make a definitive conclusion.

Example Calculation

Let’s assume the river is 50 meters wide (d = 50) and the current speed is 2 m/s (v_c = 2). We can calculate:

• Time_A = 2 * 50 / 10 = 10 seconds
• Time_B = 100 / (10 + 2) + 100 / (10 - 2)
• Time_B = 100 / 12 + 100 / 8
• Time_B = 8.33 + 12.5 = 20.83 seconds

In this case, A would win with a time of 10 seconds compared to B's 20.83 seconds.

Final Thoughts

The outcome of the race depends heavily on the width of the river and the speed of the current. If you have specific values for these variables, we can calculate the exact times and determine the winner more accurately. In general, A's direct path often proves to be faster unless the current is significantly strong, which could affect B's return time considerably.