Dr. Lin is working a 12-hour shift at the hospital. She has already worked 9
3
4
hours. After taking a
1
4
-hour break, Dr. Lin splits her remaining time equally among her last 4 patients. How much time does Dr. Lin spend with each patient?

To determine how much time Dr. Lin spends with each patient, let's break down the problem step by step:

1. **Total shift time**: Dr. Lin works a 12-hour shift.

2. **Time already worked**: Dr. Lin has already worked \(9 \frac{3}{4}\) hours. This can be converted to an improper fraction or decimal:
   \[
   9 \frac{3}{4} = 9 + \frac{3}{4} = 9.75 \text{ hours}
   \]

3. **Break time**: Dr. Lin takes a \( \frac{1}{4} \) hour break.

4. **Remaining time after the break**: Subtract the time already worked and the break time from the total shift time:
   \[
   \text{Remaining time} = 12 - 9.75 - 0.25
   \]
   \[
   \text{Remaining time} = 12 - 10 = 2 \text{ hours}
   \]

5. **Time spent with each patient**: Dr. Lin splits this remaining time equally among her last 4 patients. Therefore, the time spent with each patient is:
   \[
   \text{Time per patient} = \frac{2 \text{ hours}}{4} = 0.5 \text{ hours} = 30 \text{ minutes}
   \]

Dr. Lin spends **30 minutes** with each patient.

Would you like further details or have any questions?

Here are some related questions:
1. What is the total time Dr. Lin spends working if she also sees 2 more patients after the break?
2. If Dr. Lin had taken a longer break, how would that affect the time spent with each patient?
3. How much time does Dr. Lin spend with each patient if she had 5 patients instead of 4?
4. If Dr. Lin had 1 hour left instead of 2 hours, how would the time spent per patient change?
5. What if Dr. Lin's shift was extended by an hour, how would this affect the time spent per patient?

**Tip:** When working with time, converting mixed numbers to decimals or improper fractions can simplify calculations.

Discover how Dr. Lin allocates her time during a 12-hour hospital shift. Solve the problem step-by-step: determine total shift time, subtract time worked and breaks, and find out how much time Dr. Lin spends with each patient. Suitable for students in Grades 5-7 learning fraction arithmetic and time calculations.

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