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Understanding relative velocity is crucial when dealing with motion that involves more than one object or reference frame. It is the velocity of an object as observed from a particular frame of reference, and is a vector quantity, which means it has both magnitude and direction. The concept is especially important in river velocity problems, such as the scenario with the two friends traveling from pier A to pier B and back.

When the rower moves downstream, the river aids his motion, so we add the river's velocity to his rowing speed relative to the water. Conversely, moving upstream, the river resists his rowing, so we subtract the river's velocity from his rowing speed. This mathematical manipulation is essential for determining the rower’s true speed relative to the shore, which is the stationary frame of reference in our problem.

Motion in a straight line, also known as rectilinear motion, is the simplest form of motion and is as the name suggests - movement along a straight path. In the given problem, the friends are traveling in straight paths between the two piers. It is important to consider that in such motion, the distance covered is equal to the magnitude of displacement only when there is no change in direction. Since the friends travel to pier B and then return to pier A, their round trip can be seen as two separate instances of straight-line motion, one downstream and one upstream.

Speed and distance calculations are foundational concepts in physics, enabling us to solve problems relating to travel and movement. The speed is a measure of how fast an object is moving and is the rate at which the object covers a distance. Distance is the total path length traveled by an object.

In our example, both speed and distance affect the total time taken for the trips. The walking friend’s speed remains constant for the entire journey, making his calculations straightforward. For the rower, different speeds must be used for each leg of the trip, as the river's current affects the rowing speed differently depending on the direction of travel. Once you find the individual leg times, by calculating the distance divided by the respective speed, you can sum them up to find the total time for the round trip.

Round trip time computation entails calculating the total time required to go from a starting point to a destination and back again. In our exercise, we must account for both the downstream and upstream trips separately, as they require different amounts of time due to the varying conditions of the river velocity affecting the rower's speed.

To compute the time for each leg, we use the formula:
\( \text{time} = \frac{\text{distance}}{\text{speed}} \)
This calculation is done twice, once for each direction. For the walker, with constant speed, it's a simple matter, while for the rower, careful consideration of the relative velocity between the river and the rowboat is required. After finding the upstream and downstream times, we add them together to yield the total round trip time for each individual. This is an essential procedure in problems involving return journeys where conditions affecting speed may differ in each direction of travel.