Speed of the River's Current Puzzle

What is the puzzle about the speed of the river's current?

Given the information that Mary Joy can paddle her kayak 6 miles per hour in still water, and it takes her as long to paddle 12 miles upstream as it takes her to travel 36 miles downstream, what can we determine about the speed of the river's current?

Answer:

The speed of the river's current is 2 miles per hour.

The puzzle is based on the speed at which Mary Joy can paddle her kayak in still water and the time it takes for her upstream and downstream journeys. By setting up and solving an equation involving her upstream and downstream journeys, we can determine the speed of the river's current.

Mary Joy's speed in still water is 6 miles per hour. To determine the speed of the river's current, we need to analyze her upstream and downstream journeys.

Let's assume the speed of the current is x miles per hour. When kayaking upstream, Mary Joy's speed relative to the water is 6 - x miles per hour (since she's moving against the current).

The time it takes for her to paddle 12 miles upstream is the distance divided by her speed: 12 / (6 - x) hours. When kayaking downstream, Mary Joy's speed relative to the water is 6 + x miles per hour (since she's moving with the current).

The time it takes for her to travel 36 miles downstream is the distance divided by her speed: 36 / (6 + x) hours. Since the time for the upstream journey is equal to the time for the downstream journey, we can set up the equation: 12 / (6 - x) = 36 / (6 + x).

By solving the equation, we find that x = 2 miles per hour. Therefore, the speed of the river's current is 2 miles per hour.