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?

Question

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.