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 determi

Question

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

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5 months 2021-08-09T15:51:22+00:00 2 Answers 42 views 0

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)

Step-by-step 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

2. 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.