I believe that this question is asking a straightforward velocity and distance question without having to calculate for things like friction and rates of acceleration and deceleration of the boat. The reason that I have to assume this is because the question does not mention how long the boat took to accelerate to its stated rate of travel. Additionally, turning around could affect the overall final location of the boat. For example, did the boat turn around in a big "U" shape, or did it spin a 180 degree turn in a specific location? My answer is going to assume that the boat was already moving at the 5 knot speed when the timing began, and the boat "magically" turned around on the spot and was immediately traveling downstream at 2 knots for the stated duration.
If the boat is traveling at 5 knots upstream and the stream is flowing in the opposite direction at 2 knots, the boat is moving upstream at a speed of 3 knots relative to the shore. The velocities are subtracted from each other because they are moving in opposite directions. 5-2=3.
Distance traveled at a constant speed can be calculated by using the following equation: Distance = Rate x Time.
Distance = 3 knots x 20 minutes
Some work needs to be done on the initial setup because knots is a rate of travel using hours, and the boat was timed in minutes. You could convert 3 knots to meters per minute (92.6 meters/min) or to miles per minute (.0575 mi/min). The goal is to get the knots time unit to be in minutes. Conversely, you could convert minutes to hours. This is more straightforward. 20 minutes is 1/3 of an hour (.3333333333 hours). Keep in mind that in all of these cases, you are forced to round off somewhere, so each answer is going to vary slightly from a direct comparison with the other calculations.
Distance = 92.6 meters/min x 20 minutes
Distance = 1,852 meters
Distance = .0575 mi/min x 20 minutes
Distance = 1.15 miles
Distance = 3 knots x .33 hours
Distance = .99 nautical miles (upstream)
Whichever unit you choose to work with, that is how far upstream the boat traveled. Use the same equation setup for how far the boat will travel downstream at a speed of 2 knots for 10 minutes (1/6 of an hour).
Since the boat's speed is given in knots, I will stick to calculating distances in nautical miles.
Distance = 2 knots x .167 hours
Distance = .334 nautical miles (downstream)
The boat went upstream first and travelled .99 nautical miles. It then floated back downstream .334 nautical miles. That means the total upstream travel is .99 - .334. That comes out to .656 nautical miles upstream from the original launch location.
Of course, the entire answer will change if the boat is actually traveling at at speed of 5 knots relative to the shore at the beginning of the problem.
Distance = 5 knots x .33 hours
Distance = 1.65 nautical miles
1.65 nautical miles upstream - .334 nautical miles downstream = 1.316 nautical miles upstream from the original launch location.
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