Adding and Subtracting Time Worksheets - Free Printable

The task involves adding and subtracting time in hours, minutes, and seconds. Below is a step-by-step explanation of how to solve each problem.

General Approach:

1. Align the units: Ensure that you are adding or subtracting hours with hours, minutes with minutes, and seconds with seconds.
2. Perform the operation:
- For addition: Add the hours, minutes, and seconds separately.
- For subtraction: Subtract the hours, minutes, and seconds separately.
3. Handle overflow/underflow:
- If the seconds exceed 60, convert the excess into minutes.
- If the minutes exceed 60, convert the excess into hours.
- If the minutes go below 0, borrow from the hours.
- If the seconds go below 0, borrow from the minutes.

Detailed Solutions:

#### Problem 1: Add 23 hours, 45 minutes, 20 seconds + 1 hour, 30 minutes, 40 seconds
- Hours: \( 23 + 1 = 24 \)
- Minutes: \( 45 + 30 = 75 \) (75 minutes = 1 hour and 15 minutes)
- Seconds: \( 20 + 40 = 60 \) (60 seconds = 1 minute)

Adjust for overflow:
- Add the extra hour from minutes to hours: \( 24 + 1 = 25 \)
- Add the extra minute from seconds to minutes: \( 15 + 1 = 16 \)

Final answer: 25 hours, 16 minutes, 0 seconds

#### Problem 2: Subtract 23 hours, 45 minutes, 20 seconds - 1 hour, 30 minutes, 40 seconds
- Hours: \( 23 - 1 = 22 \)
- Minutes: \( 45 - 30 = 15 \)
- Seconds: \( 20 - 40 \) (seconds go negative, so borrow 1 minute = 60 seconds)

Adjust for underflow:
- Borrow 1 minute from minutes: \( 15 - 1 = 14 \)
- Add 60 seconds to the seconds: \( 20 + 60 - 40 = 40 \)

Final answer: 22 hours, 14 minutes, 40 seconds

#### Problem 3: Add 12 hours, 30 minutes, 45 seconds + 28 hours, 20 minutes, 15 seconds
- Hours: \( 12 + 28 = 40 \)
- Minutes: \( 30 + 20 = 50 \)
- Seconds: \( 45 + 15 = 60 \) (60 seconds = 1 minute)

Adjust for overflow:
- Add the extra minute from seconds to minutes: \( 50 + 1 = 51 \)

Final answer: 40 hours, 51 minutes, 0 seconds

#### Problem 4: Subtract 12 hours, 30 minutes, 45 seconds - 28 hours, 20 minutes, 15 seconds
- Hours: \( 12 - 28 \) (hours go negative, so borrow 1 day = 24 hours)
- Minutes: \( 30 - 20 = 10 \)
- Seconds: \( 45 - 15 = 30 \)

Adjust for underflow:
- Borrow 1 day from hours: \( 12 + 24 - 28 = 8 \)

Final answer: 8 hours, 10 minutes, 30 seconds

#### Problem 5: Add 13 hours, 12 minutes, 3 seconds + 29 hours, 45 minutes, 27 seconds
- Hours: \( 13 + 29 = 42 \)
- Minutes: \( 12 + 45 = 57 \)
- Seconds: \( 3 + 27 = 30 \)

No overflow or underflow.

Final answer: 42 hours, 57 minutes, 30 seconds

#### Problem 6: Subtract 13 hours, 12 minutes, 3 seconds - 29 hours, 45 minutes, 27 seconds
- Hours: \( 13 - 29 \) (hours go negative, so borrow 1 day = 24 hours)
- Minutes: \( 12 - 45 \) (minutes go negative, so borrow 1 hour = 60 minutes)
- Seconds: \( 3 - 27 \) (seconds go negative, so borrow 1 minute = 60 seconds)

Adjust for underflow:
- Borrow 1 day from hours: \( 13 + 24 - 29 = 8 \)
- Borrow 1 hour from minutes: \( 12 + 60 - 45 = 27 \)
- Borrow 1 minute from seconds: \( 3 + 60 - 27 = 36 \)

Final answer: 8 hours, 27 minutes, 36 seconds

#### Problem 7: Add 23 hours, 45 minutes, 20 seconds + 27 hours, 30 minutes, 40 seconds
- Hours: \( 23 + 27 = 50 \)
- Minutes: \( 45 + 30 = 75 \) (75 minutes = 1 hour and 15 minutes)
- Seconds: \( 20 + 40 = 60 \) (60 seconds = 1 minute)

Adjust for overflow:
- Add the extra hour from minutes to hours: \( 50 + 1 = 51 \)
- Add the extra minute from seconds to minutes: \( 15 + 1 = 16 \)

Final answer: 51 hours, 16 minutes, 0 seconds

#### Problem 8: Subtract 23 hours, 45 minutes, 20 seconds - 27 hours, 30 minutes, 40 seconds
- Hours: \( 23 - 27 \) (hours go negative, so borrow 1 day = 24 hours)
- Minutes: \( 45 - 30 = 15 \)
- Seconds: \( 20 - 40 \) (seconds go negative, so borrow 1 minute = 60 seconds)

Adjust for underflow:
- Borrow 1 day from hours: \( 23 + 24 - 27 = 20 \)
- Borrow 1 minute from seconds: \( 20 + 60 - 40 = 40 \)

Final answer: 20 hours, 15 minutes, 40 seconds

Final Answers:

1. 25 hours, 16 minutes, 0 seconds
2. 22 hours, 14 minutes, 40 seconds
3. 40 hours, 51 minutes, 0 seconds
4. 8 hours, 10 minutes, 30 seconds
5. 42 hours, 57 minutes, 30 seconds
6. 8 hours, 27 minutes, 36 seconds
7. 51 hours, 16 minutes, 0 seconds
8. 20 hours, 15 minutes, 40 seconds

\boxed{
\begin{array}{ll}
1. & 25 \text{ hours, } 16 \text{ minutes, } 0 \text{ seconds} \\
2. & 22 \text{ hours, } 14 \text{ minutes, } 40 \text{ seconds} \\
3. & 40 \text{ hours, } 51 \text{ minutes, } 0 \text{ seconds} \\
4. & 8 \text{ hours, } 10 \text{ minutes, } 30 \text{ seconds} \\
5. & 42 \text{ hours, } 57 \text{ minutes, } 30 \text{ seconds} \\
6. & 8 \text{ hours, } 27 \text{ minutes, } 36 \text{ seconds} \\
7. & 51 \text{ hours, } 16 \text{ minutes, } 0 \text{ seconds} \\
8. & 20 \text{ hours, } 15 \text{ minutes, } 40 \text{ seconds} \\
\end{array}
}