To determine who worked at the highest intensity level during their spin class, we need to compare how close each friend's average heart rate of 172 beats per minute (bpm) is relative to their individual heart rate zone.
First, let's define the intensity level for each person as the ratio of their average heart rate above the minimum value of their target heart rate zone to the total range of their target heart rate zone.
Here is how we can calculate the intensity level for each person:
1. Jeff's target heart rate zone: 135 bpm - 175 bpm
- Range: 175 - 135 = 40 bpm
- Intensity level: (172 - 135) / 40 = 37 / 40 = 0.925
2. Mike's target heart rate zone: 145 bpm - 188 bpm
- Range: 188 - 145 = 43 bpm
- Intensity level: (172 - 145) / 43 = 27 / 43 ≈ 0.6279
3. Ty's target heart rate zone: 140 bpm - 180 bpm
- Range: 180 - 140 = 40 bpm
- Intensity level: (172 - 140) / 40 = 32 / 40 = 0.8
4. Liam's target heart rate zone: 140 bpm - 183 bpm
- Range: 183 - 140 = 43 bpm
- Intensity level: (172 - 140) / 43 = 32 / 43 ≈ 0.7442
Now, let's compile the intensity levels:
- Jeff: 0.925
- Mike: 0.6279
- Ty: 0.8
- Liam: 0.7442
Comparing these values, we see that Jeff has the highest intensity level of 0.925.
Thus, based on their average heart rate and their target heart rate zones, Jeff worked at the highest intensity level during the spin class.
