On the way to school, a student rides his bike to the bus stop. He then waits a few minutes for the bus to come and rides the bus to school. The bus stops at school, and he walks from the parking lot to his first class. Is the graph of his distance always increasing? Explain.

Answer 1

The graph of the student's distance from home or the starting point is not always increasing throughout his journey to school. Let's break down the different segments of his trip:

1. Riding the bike to the bus stop: During this segment, his distance from home is increasing as he moves away from home towards the bus stop.

2. Waiting for the bus: While the student waits for the bus, he remains at the same location (the bus stop), so his distance from home does not change. The graph of his distance here would be flat (constant).

3. Riding the bus to school: When the bus starts moving, the student's distance from home increases again as the bus travels further away from home.

4. Walking from the parking lot to his first class: After the bus arrives at school, the student gets off and walks to his class. Since the school is also farther from home than the bus stop, his distance overall continues to increase during this walk.

However, if we consider the entire journey from the start at home to the end at school, the distance does not decrease at any point overall. It only remains constant while waiting for the bus and continually increases during biking and bus riding.

Thus, while the graph is not entirely "always increasing" in the strict sense (due to the waiting period), the student is not ever moving closer to home after starting his journey. The overall trend in distance is that it is never decreasing.