Question

cheyenne, naty, and paul have a 10 km bicycle race after school. their race results are shown in the time - distance graph below. use the graph to fill in the table of race results, calculate average speeds, and answer the questions.

1. who kept a constant speed in the race?
2. who won the race?
3. who got second place?
4. who was winning the race in the beginning?

Explanation:

Step1: Extract data from graph

From the time-distance graph:

• Paul: Total Distance = 10 km, Total Time = 60 minutes
• Cheyenne: Total Distance = 10 km, Total Time = 45 minutes
• Naty: Total Distance = 10 km, Total Time = 50 minutes

Step2: Calculate average speed

Average speed formula: $\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$

• Paul: $\frac{10}{60} = \frac{1}{6} \approx 0.167$ km/min
• Cheyenne: $\frac{10}{45} = \frac{2}{9} \approx 0.222$ km/min
• Naty: $\frac{10}{50} = 0.2$ km/min

Step3: Identify constant speed

A straight line on the graph means constant speed. Paul's line is straight.

Step4: Determine race rankings

Ranking by total time (shorter time = faster):

1. Cheyenne (45 min), 2. Naty (50 min), 3. Paul (60 min)

Step5: Identify early race leader

At 15 minutes, Paul traveled 5 km, which is farther than Cheyenne/Naty's distance at that time.

Answer:

Filled Table:

Cyclist	Total Distance	Total Time	Average Speed
Cheyenne	10 km	45 minutes	$\frac{2}{9}$ km/min (≈0.222 km/min)
Naty	10 km	50 minutes	0.2 km/min

1. Who kept a constant speed in the race? Paul
2. Who won the race? Cheyenne
3. Who got second place? Naty
4. Who was winning the race in the beginning? Paul