Question

William is in the middle of swimming in a ten-mile race. He swims at a steady speed, and then slows down, stops to eat, swims faster to get back in the race, and returns to a steady speed. He later stops for water, and then again swims faster to get back in the race. Which graph best represents the situation?

A. A graph with time on the x-axis and speed on the y-axis. The graph is constant, decreases to 0, increases, is constant, decreases to 0, and then increases.

B. A graph with time on the x-axis and speed on the y-axis. The graph decreases, is constant at 0, increases, is constant, decreases to 0, and then increases.

C. A graph with time on the x-axis and speed on the y-axis. The graph is constant, decreases to 0, is constant, increases, decreases to 0, and then increases.

D. A graph with time on the x-axis and speed on the y-axis. The graph is constant, decreases to 0, is constant, increases, and then is constant.

Answer 1

To analyze William's swimming pattern in the ten-mile race, we can break down his actions:

1. **Steady speed**: This would be represented as a horizontal line on the graph where the speed remains constant.
2. **Slowing down**: This would show a decrease in speed until it reaches 0.
3. **Stopping to eat**: This would also represent a period where speed is constant at 0.
4. **Swimming faster to get back in the race**: This would show an increase in speed from 0 to a faster rate.
5. **Returning to steady speed**: After swimming faster, there would be another horizontal line showing constant speed.
6. **Stopping for water**: Again, this would represent a period where speed is constant at 0.
7. **Swimming faster again**: Lastly, there would be an increase in speed as he swims faster again.

Given these observations, let's evaluate the options:

- **Option A** has the sequence: constant, decreases to 0, increases, is constant, decreases to 0, and then increases.
- **Option B** features: decreases, is constant at 0, increases, is constant, decreases to 0, and then increases.
- **Option C** describes: constant, decreases to 0, is constant, increases, decreases to 0, and then increases.
- **Option D** follows the path: constant, decreases to 0, is constant, increases, and then is constant.

The best representation of William's situation is **Option C** because it reflects first a steady speed, then a slow down to 0 (stopping), constant at 0 (eating), an increase in speed (swimming faster), another steady speed (swimming normally), stopping again (for water), and then increasing speed (swimming faster again).

Thus, the correct graph is **C**.