Answer:
To estimate the blood alcohol concentration (BAC) for a 160 lb man and a 140 lb man who drank 5 drinks over 3 hours, we can use the Widmark formula:
BAC = (Alcohol consumed in grams / (Body weight in grams × r)) - (Metabolism rate × hours)
Where:
- r is the alcohol distribution ratio (typically 0.68 for men).
- The metabolism rate is about 0.015 BAC per hour.
Assuming each drink contains about 14 grams of pure alcohol (roughly equivalent to a standard drink), they each consumed 70 grams of alcohol (5 drinks × 14 grams).
For the calculations:
1. Convert body weight to grams:
- 160 lbs = 72,575 grams
- 140 lbs = 63,502 grams
2. Calculate initial BAC:
- For the 160 lb man:
BAC = (70 / (72,575 × 0.68)) - (0.015 × 3)
= (70 / 49,757.4) - 0.045
= 0.0014 - 0.045 ≈ -0.0436 (effectively 0.000, as BAC cannot be negative)
- For the 140 lb man:
BAC = (70 / (63,502 × 0.68)) - (0.015 × 3)
= (70 / 43,581.36) - 0.045
= 0.0016 - 0.045 ≈ -0.0434 (effectively 0.000)
However, these values suggest an over-simplification, as actual BAC might be influenced by factors like metabolism, drinking speed, food intake, and individual tolerance.
**Symptoms**:
- BAC around 0.02-0.05: Mild relaxation, slight impairment of judgment.
- Higher BAC levels may lead to increased impairment, with potential dizziness or coordination issues.
In practice, if both individuals had some time to metabolize the alcohol, their BAC would likely be low to moderate, with minimal to mild symptoms.
