Determining the Speed of a River's Current

How can we calculate the speed of a river's current based on Dwayne's situation?

What is Dwayne's paddling speed in still water and how does it relate to his paddling speed upstream and downstream?

Paddle Speed Calculation:

In order to calculate the speed of a river's current in Dwayne's scenario, we need to understand the relationship between his paddling speed in still water, his effective speeds upstream and downstream, and the time taken for each direction of paddling.

In this particular case, Dwayne can paddle his kayak at a speed of 5 miles per hour in still water. When paddling upstream (against the current), his effective speed decreases since he is paddling against the flow of the river. Conversely, when paddling downstream (with the current), his effective speed increases due to the added assistance from the river's current.

By utilizing the principles of relative velocity in Newtonian Mechanics, we can set up equations based on the distances traveled upstream and downstream, and the time taken for each scenario. Equating these equations allows us to solve for the speed of the river's current, denoted as 'c'.

Let's denote Dwayne's paddling speed in still water as 5 mph. The equation representing his upstream paddling speed is (5 - c) and the equation for his downstream paddling speed is (5 + c). The time taken for both scenarios is denoted as 't'.

Creating equations based on the distances traveled upstream and downstream:
For traveling upstream: 9 = (5 - c) x t
For traveling downstream: 21 = (5 + c) x t

By equating these two equations and solving for 'c', we can determine the speed of the river's current, which in this case is 1.5 mph. This calculation allows us to understand the impact of the river's current on Dwayne's paddling speed and overall journey time.