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.

cyclist | total distance | total time | average speed
--- | --- | --- | ---
paul | | |
cheyenne | | |
naty | | |

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

• Paul: Total Distance = 10 km, Total Time = 60 minutes
• Cheyenne: Total Distance = 10 km, Total Time = 50 minutes
• Naty: Total Distance = 10 km, Total Time = 55 minutes

Step2: Calculate average speed

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

• Paul: $\frac{10}{60} = \frac{1}{6} \approx 0.17$ km/min
• Cheyenne: $\frac{10}{50} = 0.2$ km/min
• Naty: $\frac{10}{55} = \frac{2}{11} \approx 0.18$ km/min

Step3: Identify constant speed

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

Step4: Determine race rankings

Shorter time = faster finish: Cheyenne (50 min) < Naty (55 min) < Paul (60 min)

Step5: Identify early race leader

At 15 minutes, Paul traveled 5 km, more than Naty (0 km) and Cheyenne (0 km).

Answer:

Completed Table:

Cyclist	Total Distance	Total Time	Average Speed
Cheyenne	10 km	50 minutes	$0.2$ km/min
Naty	10 km	55 minutes	$\frac{2}{11}$ km/min (≈0.18 km/min)

1. Paul
2. Cheyenne
3. Naty
4. Paul