Calculating the Speed of the River Current for Rick's Kayaking Trip
Rick's Kayaking Adventure
Rick paddled up the river, spent the night camping, and then paddled back. He spent 8 hours paddling and the campground was 15 miles away. If Rick kayaked at a speed of 4 mph, what was the speed of the current (in mph)?
Final answer:
To find the speed of the river current, two equations representing Rick's time paddling upstream and downstream were formulated and solved to find that the speed of the current is 1 mph.
Explanation:
Calculating the Speed of the River Current
To determine the speed of the current, we would need to use the principle that the actual speed of a boat paddling upstream against a current is decreased by the speed of the current, while the speed downstream is increased by the speed of the current. Let's denote the speed of the current as c mph. When Rick paddles up the river against the current, his effective speed would be (4 - c) mph, and while going downstream with the current, his speed would be (4 + c) mph. Since the campground is 15 miles away, and he spent 8 hours paddling both ways, we can set up two equations to represent the time spent going each way:
- Time upstream = Distance / Speed upstream
- Time downstream = Distance / Speed downstream
We know that the sum of the two times is 8 hours (Time upstream + Time downstream = 8). By plugging in the distances and speeds, we get the following:
- Time upstream = 15 / (4 - c)
- Time downstream = 15 / (4 + c)
Adding both equations gives us 15 / (4 - c) + 15 / (4 + c) = 8. To find the value of c, we solve this equation.
After calculating, we find that the speed of the current c is 1 mph.