# Kayaker's Speed in Calm Water Calculation

## Question:

A kayaker paddles straight into a 4-mph current and travels for 3 miles then turns around and paddles straight back to the starting point. It takes 1 hour to complete the trip. How fast does she travel in calm water?

## Answer:

The kayaker's speed in calm water is 2 mph.

The kayaker's speed in calm water can be calculated based on her total distance traveled and time taken, considering the effect of the current on her effective speed. To determine her speed in calm water, we need to understand the concept of effective speed when paddling against or with the current.

When the kayaker is paddling against the current, her effective speed is her speed minus the current's speed. Conversely, when paddling with the current, her effective speed is her speed plus the current's speed. Since she covers a total distance of 6 miles (3 miles forth and 3 miles back) in 1 hour, her overall average speed is 6 mph.

We can set up the following equation to solve for her speed in calm waters: (x-4) + (x+4) = 6 mph, where x represents her speed in calm water. By solving the equation, we find that x = 2 mph.

Understanding and applying the concept of speed calculation allows us to determine the kayaker's speed in calm water accurately. This type of problem helps in grasping the impact of currents on speed and the importance of accounting for such factors in real-world scenarios.