To determine who had a head start and by how much, we first need to compare the data sets for Nina and Ryan.
From the coordinate plane data:
- Nina's distances are:
- At 4 seconds: 32 meters
- At 6 seconds: 48 meters
- At 8 seconds: 64 meters
- At 10 seconds: 80 meters
From the table data (assumed to be Ryan's distances):
- Ryan's distances are:
- At 4 seconds: 35 meters
- At 6 seconds: 47.5 meters
- At 8 seconds: 60 meters
We can analyze the distances covered by both runners at the same time points to find out who had a head start.
At 4 seconds:
- Nina: 32 meters
- Ryan: 35 meters
Ryan is ahead of Nina by 3 meters at 4 seconds.
At 6 seconds:
- Nina: 48 meters
- Ryan: 47.5 meters
Nina is ahead of Ryan by 0.5 meters at 6 seconds.
At 8 seconds:
- Nina: 64 meters
- Ryan: 60 meters
Nina is ahead of Ryan by 4 meters at 8 seconds.
However, since the question is asking specifically who had a head start, we should focus on the beginning of the race (time = 0 seconds). Because Ryan is ahead at the 4-second mark but is not consistently ahead later, it might imply a head start.
By calculating the trend:
- To see if Ryan had a head start, let's establish the constant speeds:
- Nina's speed can be calculated using the difference between any two points:
- Between 6 seconds and 4 seconds: (48-32) / (6-4) = 16/2 = 8 meters/second.
- Similarly, between other points, it's evident that Nina's speed is consistently 8 meters/second.
- Ryan's speed calculation:
- Between 6 seconds and 4 seconds: (47.5-35) / (6-4) = 12.5/2 = 6.25 meters/second.
- From 6 to 8 seconds: (60-47.5) / (8-6) = 12.5/2 = 6.25 meters/second.
Ryan's speed is consistently 6.25 meters/second.
Ryan had traveled 35 meters in 4 seconds, maintaining a speed of 6.25 meters/second:
- Ryan's position can be traced back to time zero:
- If Ryan runs at 6.25 meters per second, in 4 seconds he would cover 4 * 6.25 = 25 meters from any starting point.
- Since Ryan covered 35 meters in 4 seconds, to find the initial distance at 0 seconds:
35 meters - 25 meters = 10 meters head start.
Therefore, Ryan had a head start of 10 meters.
Ryan had a head start of 10 meters.
A coordinate plane showing Nina's run. The x-axis shows Time in seconds and the y-axis shows Distance in meters. Four points plotted and labeled. The points are (4, 32), (6, 48), (8, 64), (10, 80). A two column table with four rows. The first column, Time in seconds, has the entries, 4, 6, 8. The second column, Distance in meters, has the entries, 35, 47.5, 60.
Nina and Ryan each ran at a constant speed for a 100-meter race. Each runner’s distance for the same section of the race is displayed on the left. Who had a head start, and how big was the head start?
had a head start of
meter
1 answer