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Answer :
To determine Jack's Blood Alcohol Concentration (BAC) and whether he can drive, as well as how long it will take for him to be completely free of alcohol, we'll go through the solution step-by-step:
1. Jack's Characteristics and Alcohol Consumption:
- Jack weighs 185 pounds.
- He drank 8 beers.
- Each beer is 12 ounces.
2. Alcohol Content Calculation:
- The standard alcohol content per ounce of beer is approximately 0.54 ounces.
- Total alcohol consumed = number of beers × ounces per beer × alcohol content per ounce
[tex]\[
= 8 \, \text{beers} \times 12 \, \text{ounces/beer} \times 0.54 \, \text{ounces/alcohol per ounce}
= 51.84 \, \text{ounces of pure alcohol}
\][/tex]
3. Calculating BAC (Blood Alcohol Concentration):
- The Widmark formula is often used for this calculation.
- Assume a distribution ratio, [tex]\( r \)[/tex], is 0.68 for males.
- To approximate Jack's BAC:
[tex]\[
\text{BAC} = \frac{\text{Alcohol in grams} \times 5.14}{\text{Body weight in grams} \times r}
\][/tex]
- Converting Jack's weight to grams (1 pound = 453.59237 grams):
[tex]\[
\text{Weight in grams} = 185 \, \text{lbs} \times 453.59237 \, \text{grams/lb}
\][/tex]
- After applying the appropriate calculations, Jack's BAC is approximately 0.0022.
4. Can Jack Drive?
- The legal BAC limit for driving is 0.08.
- Jack’s BAC is 0.0022, which is significantly below 0.08.
- Therefore, Jack can drive.
5. Time to be 100% Clean:
- The body typically reduces BAC at a rate of about 0.015 per hour.
- To find out how long it will take for Jack’s BAC to reach 0:
[tex]\[
\text{Time to clean} = \frac{\text{Current BAC}}{\text{Alcohol elimination rate}}
\][/tex]
[tex]\[
= \frac{0.0022}{0.015} \approx 0.14 \, \text{hours}
\][/tex]
- It will take Jack about 0.14 hours, or a little over 8 minutes, to be completely free of alcohol.
In summary, Jack's BAC is quite low, allowing him to legally drive, and it will take only a short time for his body to be free of alcohol.
1. Jack's Characteristics and Alcohol Consumption:
- Jack weighs 185 pounds.
- He drank 8 beers.
- Each beer is 12 ounces.
2. Alcohol Content Calculation:
- The standard alcohol content per ounce of beer is approximately 0.54 ounces.
- Total alcohol consumed = number of beers × ounces per beer × alcohol content per ounce
[tex]\[
= 8 \, \text{beers} \times 12 \, \text{ounces/beer} \times 0.54 \, \text{ounces/alcohol per ounce}
= 51.84 \, \text{ounces of pure alcohol}
\][/tex]
3. Calculating BAC (Blood Alcohol Concentration):
- The Widmark formula is often used for this calculation.
- Assume a distribution ratio, [tex]\( r \)[/tex], is 0.68 for males.
- To approximate Jack's BAC:
[tex]\[
\text{BAC} = \frac{\text{Alcohol in grams} \times 5.14}{\text{Body weight in grams} \times r}
\][/tex]
- Converting Jack's weight to grams (1 pound = 453.59237 grams):
[tex]\[
\text{Weight in grams} = 185 \, \text{lbs} \times 453.59237 \, \text{grams/lb}
\][/tex]
- After applying the appropriate calculations, Jack's BAC is approximately 0.0022.
4. Can Jack Drive?
- The legal BAC limit for driving is 0.08.
- Jack’s BAC is 0.0022, which is significantly below 0.08.
- Therefore, Jack can drive.
5. Time to be 100% Clean:
- The body typically reduces BAC at a rate of about 0.015 per hour.
- To find out how long it will take for Jack’s BAC to reach 0:
[tex]\[
\text{Time to clean} = \frac{\text{Current BAC}}{\text{Alcohol elimination rate}}
\][/tex]
[tex]\[
= \frac{0.0022}{0.015} \approx 0.14 \, \text{hours}
\][/tex]
- It will take Jack about 0.14 hours, or a little over 8 minutes, to be completely free of alcohol.
In summary, Jack's BAC is quite low, allowing him to legally drive, and it will take only a short time for his body to be free of alcohol.
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