Elapsed Time Worksheets - Math Monks - Free Printable

To solve the problem of determining how much time has elapsed between two given times, we need to calculate the difference between the end time and the start time. Here's a step-by-step explanation for each question:

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General Approach:

1. Same Day Calculation:
- If both times are on the same day (e.g., AM to AM or PM to PM), subtract the start time from the end time.
- If the subtraction results in a negative value, adjust by adding 12 hours (for AM/PM conversion).

2. Crossing Midnight:
- If the start time is in AM and the end time is in PM (or vice versa), calculate the time elapsed in two parts:
- From the start time to midnight.
- From midnight to the end time.
- Add these two parts together.

3. Formatting the Result:
- Express the result in hours and minutes.

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Solutions:

#### 1. From 3:45 AM to 6:15 AM
- Both times are in AM.
- Elapsed time = \( 6:15 - 3:45 \)
- Subtract directly:
- Hours: \( 6 - 3 = 3 \)
- Minutes: \( 15 - 45 = -30 \) (borrow 1 hour = 60 minutes)
- Adjust: \( 3 - 1 = 2 \) hours, \( 60 + 15 - 45 = 30 \) minutes
- Answer: 2 hours 30 minutes

#### 2. From 1:30 PM to 4:40 PM
- Both times are in PM.
- Elapsed time = \( 4:40 - 1:30 \)
- Subtract directly:
- Hours: \( 4 - 1 = 3 \)
- Minutes: \( 40 - 30 = 10 \)
- Answer: 3 hours 10 minutes

#### 3. From 12:20 PM to 6:00 PM
- Both times are in PM.
- Elapsed time = \( 6:00 - 12:20 \)
- Subtract directly:
- Hours: \( 6 - 12 = -6 \) (add 12 hours)
- Adjust: \( 6 - 0 = 6 \) hours, \( 0 - 20 = -20 \) (borrow 1 hour = 60 minutes)
- Adjust: \( 6 - 1 = 5 \) hours, \( 60 - 20 = 40 \) minutes
- Answer: 5 hours 40 minutes

#### 4. From 10:35 AM to 3:00 PM
- Start time is AM, end time is PM.
- Elapsed time:
- From 10:35 AM to 12:00 PM: \( 12:00 - 10:35 = 1 \) hour \( 25 \) minutes
- From 12:00 PM to 3:00 PM: \( 3:00 - 12:00 = 3 \) hours
- Total: \( 1 \) hour \( 25 \) minutes + \( 3 \) hours = \( 4 \) hours \( 25 \) minutes
- Answer: 4 hours 25 minutes

#### 5. From 6:00 AM to 11:20 AM
- Both times are in AM.
- Elapsed time = \( 11:20 - 6:00 \)
- Subtract directly:
- Hours: \( 11 - 6 = 5 \)
- Minutes: \( 20 - 0 = 20 \)
- Answer: 5 hours 20 minutes

#### 6. From 5:30 PM to 9:15 PM
- Both times are in PM.
- Elapsed time = \( 9:15 - 5:30 \)
- Subtract directly:
- Hours: \( 9 - 5 = 4 \)
- Minutes: \( 15 - 30 = -15 \) (borrow 1 hour = 60 minutes)
- Adjust: \( 4 - 1 = 3 \) hours, \( 60 + 15 - 30 = 45 \) minutes
- Answer: 3 hours 45 minutes

#### 7. From 11:45 PM to 2:00 AM
- Start time is PM, end time is AM (crosses midnight).
- Elapsed time:
- From 11:45 PM to 12:00 AM: \( 12:00 - 11:45 = 15 \) minutes
- From 12:00 AM to 2:00 AM: \( 2:00 - 12:00 = 2 \) hours
- Total: \( 15 \) minutes + \( 2 \) hours = \( 2 \) hours \( 15 \) minutes
- Answer: 2 hours 15 minutes

#### 8. From 1:00 AM to 5:35 AM
- Both times are in AM.
- Elapsed time = \( 5:35 - 1:00 \)
- Subtract directly:
- Hours: \( 5 - 1 = 4 \)
- Minutes: \( 35 - 0 = 35 \)
- Answer: 4 hours 35 minutes

#### 9. From 4:10 PM to 9:35 PM
- Both times are in PM.
- Elapsed time = \( 9:35 - 4:10 \)
- Subtract directly:
- Hours: \( 9 - 4 = 5 \)
- Minutes: \( 35 - 10 = 25 \)
- Answer: 5 hours 25 minutes

#### 10. From 6:35 AM to 9:40 AM
- Both times are in AM.
- Elapsed time = \( 9:40 - 6:35 \)
- Subtract directly:
- Hours: \( 9 - 6 = 3 \)
- Minutes: \( 40 - 35 = 5 \)
- Answer: 3 hours 5 minutes

#### 11. From 8:50 AM to 11:40 PM
- Start time is AM, end time is PM (crosses midnight).
- Elapsed time:
- From 8:50 AM to 12:00 PM: \( 12:00 - 8:50 = 3 \) hours \( 10 \) minutes
- From 12:00 PM to 11:40 PM: \( 11:40 - 12:00 = 11 \) hours \( 40 \) minutes
- Total: \( 3 \) hours \( 10 \) minutes + \( 11 \) hours \( 40 \) minutes = \( 14 \) hours \( 50 \) minutes
- Answer: 14 hours 50 minutes

#### 12. From 12:00 AM to 5:46 AM
- Both times are in AM.
- Elapsed time = \( 5:46 - 12:00 \)
- Subtract directly:
- Hours: \( 5 - 0 = 5 \)
- Minutes: \( 46 - 0 = 46 \)
- Answer: 5 hours 46 minutes

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Final Answers:

1. 2 hours 30 minutes
2. 3 hours 10 minutes
3. 5 hours 40 minutes
4. 4 hours 25 minutes
5. 5 hours 20 minutes
6. 3 hours 45 minutes
7. 2 hours 15 minutes
8. 4 hours 35 minutes
9. 5 hours 25 minutes
10. 3 hours 5 minutes
11. 14 hours 50 minutes
12. 5 hours 46 minutes

Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
1. & 2 \text{ hours } 30 \text{ minutes} \\
2. & 3 \text{ hours } 10 \text{ minutes} \\
3. & 5 \text{ hours } 40 \text{ minutes} \\
4. & 4 \text{ hours } 25 \text{ minutes} \\
5. & 5 \text{ hours } 20 \text{ minutes} \\
6. & 3 \text{ hours } 45 \text{ minutes} \\
7. & 2 \text{ hours } 15 \text{ minutes} \\
8. & 4 \text{ hours } 35 \text{ minutes} \\
9. & 5 \text{ hours } 25 \text{ minutes} \\
10. & 3 \text{ hours } 5 \text{ minutes} \\
11. & 14 \text{ hours } 50 \text{ minutes} \\
12. & 5 \text{ hours } 46 \text{ minutes} \\
\end{array}
}
\]