Question

You are going to calculate what speed the kayaker 's are paddling, if they stay at a constant rate the entire trip, while kayaking in Humboldt bay.

key information:

River current: 3 miles per hour
Trip distance: 2 miles (1 mile up, 1 mile back)
Total time of the trip: 3 hours 20 minutes

1) Label variables and create a table

2) Write an equation to model the problem

3) Solve the equation. Provide supporting work and detail

4) Explain the results

Answer 1

1) Variables:

- Speed of the kayaker (unknown, let's call it x)

- Speed of the current = 3 mph (given)

- Distance kayaked one way = 1 mile (given)

- Total distance covered (round trip) = 2 miles (given)

- Total time of the trip = 3 hours 20 minutes = 3.33 hours (converted to hours for convenience)

Table:

Photo attached.

2) The equation to model the problem is:

distance = rate × time

Using this equation for each kayaking portion, we get:

1 = (x - 3) t

1 = (x + 3) t

We also know that the total time of the trip is 3.33 hours:

t + t = 3.33

2t = 3.33

t = 1.665

3) Now we can solve for x by substituting t = 1.665 in either of the above equations:

1 = (x - 3) (1.665)

x - 3 = 0.599

x = 3.599

Thus, the kayakers are paddling at a speed of 3.599 miles per hour.

4) The kayakers are paddling at a speed of 3.599 miles per hour. This solution is obtained by calculating the average speed of the kayakers over the entire trip, taking into account the opposing speed of the river current. The kayakers are traveling faster downstream (with the current) than upstream (against the current).

Explanation: