Answer:
Emily won the race; she finished 1.9 seconds ahead of John.
Note: The question is incomplete. The complete question is given below:
Emily and John each ran at a constant speed for a 100-meter race. Emily gave John a 10-meter head start. Use the given data below to determine who won the race and by how many seconds.
John's run
A 2-column table with 4 rows. Column 1 is labeled Time (seconds) with entries 4, 6, 8, 10. Column 2 is labeled Distance (meters) with entries 35, 47.5, 60, 72.5.
Emily's run
A graph titled Emily's Run has time (seconds) on the x-axis and Distance (meters) on the y-axis. Points are at (4, 32), (6, 48), (8, 64), and (10, 80)
Explanation:
Step 1: Since, they ran at a constant speed, first, we calculate John's speed ;
Speed = (change in distance)/(change in time)
John's Speed = (72.5 - 60)/(10 - 8) = 6.25 m/s
Step 2: Then, we calculate Emily's speed;
Speed = (change in distance)/(change in time)
Emily's Speed = (80 - 64)/(10 - 8) = 8.00 m/s
Also, it was stated that Emily gave John a 10 m head start, therefore, John ran a distance of 90 m at 6.25 m/s while Emily ran a distance of 100 m at 8.00 m/s
Step 3: Time taken by both runners
Time = (Distance/Speed)
Time taken by John; time = (90/6.25) = 14.4 s
Time taken by Emily, Time = (100/8.00) = 12.5 s
Therefore, Emily won the race since her time to complete the race was shorter. She won the race by (14.4 - 12.5) = 1.9 s