Elapsed Time Answer Key - Complete Solutions

Master elapsed time calculations with this comprehensive answer key: finding duration, start times, and end times through 3 detailed exercises with visual infographics and step-by-step solutions.

Elapsed Time Exercises 1 to 3 - Answer Key
1 Finding Elapsed Time
Exercise 1
Sarah started reading at 2:15 PM and finished at 3:45 PM.
How long did Sarah read?
Key Definition:

Elapsed time: The amount of time that passes between two events

Elapsed Time Method:
  1. Identify the start time (2:15 PM)
  2. Identify the end time (3:45 PM)
  3. Count the hours and minutes between them
End Time
3:45 PM
Start Time
2:15 PM
Elapsed Time
1:30
Step 1: Identify start and end times

Start: 2:15 PM, End: 3:45 PM

Step 2: Count the hours

From 2:15 PM to 3:15 PM = 1 hour

Step 3: Count the remaining minutes

From 3:15 PM to 3:45 PM = 30 minutes

Step 4: Add hours and minutes together

Total elapsed time = 1 hour + 30 minutes = 1 hour 30 minutes

Correct Answer: Sarah read for 1 hour and 30 minutes
Answer Key:

✓ CORRECT: 1 hour 30 minutes

✗ INCORRECT: 1 hour 45 minutes (added 30 minutes instead of 30)

✗ INCORRECT: 2 hours (didn't count minutes)

Applied Rules:

• Subtraction: End time - Start time = Elapsed time

• Regrouping: When minutes go over 60, convert to hours

• Verification: Start time + Elapsed time = End time

Common Errors:

• Forgetting to count the minutes separately

• Adding instead of subtracting

• Not carrying over when minutes exceed 60

2 Finding End Time
Exercise 2
A movie starts at 7:20 PM and lasts for 2 hours and 15 minutes.
What time does the movie end?
Key Definition:

End time: Start time + Duration = End time

Start Time
7:20 PM
Duration
+ 2:15
End Time
9:35 PM
Step 1: Identify start time and duration

Start: 7:20 PM, Duration: 2 hours 15 minutes

Step 2: Add hours to start time

7:20 PM + 2 hours = 9:20 PM

Step 3: Add minutes to the result

9:20 PM + 15 minutes = 9:35 PM

Step 4: Verify the answer

Check: 9:35 PM - 7:20 PM = 2 hours 15 minutes ✓

Correct Answer: The movie ends at 9:35 PM
Answer Key:

✓ CORRECT: 9:35 PM

✗ INCORRECT: 9:25 PM (forgot to add 15 minutes)

✗ INCORRECT: 9:45 PM (added 25 minutes instead of 15)

Applied Rules:

• Addition: Start time + Duration = End time

• Carry over: When minutes exceed 60, add to hours

• Verification: End time - Start time = Duration

Common Errors:

• Forgetting to add the minutes

• Adding minutes incorrectly

• Not carrying over when minutes exceed 60

3 Finding Start Time
Exercise 3
A soccer game ended at 4:30 PM and lasted for 1 hour and 45 minutes.
What time did the game start?
Key Definition:

Start time: End time - Duration = Start time

End Time
4:30 PM
Duration
- 1:45
Start Time
2:45 PM
Step 1: Identify end time and duration

End: 4:30 PM, Duration: 1 hour 45 minutes

Step 2: Since 45 minutes > 30 minutes, borrow 1 hour

4:30 PM becomes 3:90 PM (borrowing 1 hour = 60 minutes)

Step 3: Subtract hours and minutes separately

Hours: 3 - 1 = 2, Minutes: 90 - 45 = 45

Step 4: Combine the results

Start time = 2:45 PM

Step 5: Verify the answer

Check: 2:45 PM + 1 hour 45 minutes = 4:30 PM ✓

Correct Answer: The game started at 2:45 PM
Answer Key:

✓ CORRECT: 2:45 PM

✗ INCORRECT: 3:15 PM (didn't borrow correctly)

✗ INCORRECT: 2:15 PM (subtracted minutes incorrectly)

Applied Rules:

• Subtraction: End time - Duration = Start time

• Borrowing: When minutes are insufficient, borrow 1 hour = 60 minutes

• Verification: Start time + Duration = End time

Common Errors:

• Forgetting to borrow when minutes are insufficient

• Subtracting minutes without borrowing

• Making arithmetic errors during subtraction

Elapsed Time Answer Key Reference
Exercise Solutions Summary
Exercise Problem Type Correct Answer Formula Used
1 Find Elapsed Time 1 hour 30 minutes End - Start = Elapsed
2 Find End Time 9:35 PM Start + Duration = End
3 Find Start Time 2:45 PM End - Duration = Start
Solution Verification Steps
1
Read the problem carefully and identify what is being asked
2
Determine the known values (start time, end time, or duration)
3
Select the appropriate formula based on what needs to be found
4
Perform the calculation step by step
5
Check your answer using the inverse operation
Common Error Patterns
  • Pattern A: Adding minutes when should subtract, or vice versa
  • Pattern B: Forgetting to borrow when subtracting minutes
  • Pattern C: Not carrying over when adding minutes exceeds 60
  • Pattern D: Mixing up AM and PM times
  • Pattern E: Misreading the clock or misinterpreting time values
End Time - Start Time = Elapsed Time
Core Formula
Start
Time
+
Duration
Elapsed
End
Time
-
Start
Time
End
Time
-
Duration
Elapsed
12
3
6
9
Advanced Elapsed Time Examples - Answer Key
4 Crossing AM/PM
Advanced Example
A train departs at 11:45 AM and arrives at 2:15 PM.
How long was the journey?
Key Concept:

Crossing noon: When time crosses from AM to PM

Step 1: Count to noon (12:00 PM)

From 11:45 AM to 12:00 PM = 15 minutes

Step 2: Count from noon to arrival

From 12:00 PM to 2:15 PM = 2 hours 15 minutes

Step 3: Add both periods

Total: 15 minutes + 2 hours 15 minutes = 2 hours 30 minutes

Correct Answer: 2 hours 30 minutes
Answer Key:

✓ CORRECT: 2 hours 30 minutes

✗ INCORRECT: 3 hours (ignored the 15 minutes in the beginning)

5 Regrouping Minutes
Advanced Example
If a task takes 1 hour 75 minutes, how do you express this?
Convert to standard time format.
Key Concept:

Regrouping: 60 minutes = 1 hour

Step 1: Identify excess minutes

75 minutes = 60 minutes + 15 minutes = 1 hour + 15 minutes

Step 2: Add to existing hours

Original 1 hour + 1 hour from regrouping = 2 hours

Step 3: Combine with remaining minutes

2 hours + 15 minutes = 2 hours 15 minutes

Correct Answer: 2 hours 15 minutes
Answer Key:

✓ CORRECT: 2 hours 15 minutes

✗ INCORRECT: 1 hour 75 minutes (not properly regrouped)

6 Multi-Day Calculation
Advanced Example
A project started on Monday at 3:00 PM and ended on Wednesday at 11:00 AM.
How long did the project last?
Key Concept:

Multi-day calculation: Calculate full days + partial days

Step 1: Calculate full days

Tuesday = 24 hours

Step 2: Calculate Monday's remaining time

From 3:00 PM to midnight = 9 hours

Step 3: Calculate Wednesday's elapsed time

From midnight to 11:00 AM = 11 hours

Step 4: Add all periods together

9 hours + 24 hours + 11 hours = 44 hours

Correct Answer: 44 hours
Answer Key:

✓ CORRECT: 44 hours

✗ INCORRECT: 32 hours (forgot Tuesday)

Elapsed Time: Detailed Summary & Key Concepts
End Time - Start Time = Elapsed Time
Core Formula
Key Time Concepts:

Elapsed Time: The amount of time that passes between two events

Start Time: When an event begins

End Time: When an event finishes

Duration: Another word for elapsed time

AM: Before noon (ante meridiem)

PM: After noon (post meridiem)

Elapsed Time Calculation Methods:
  1. Counting Method: Count forward from start time to end time
  2. Subtraction Method: End time - Start time
  3. Jump Method: Count hours first, then minutes
  4. Number Line Method: Visual representation of time passage
Tip 1: Draw a clock face to visualize the time passage.
Tip 2: When subtracting, if minutes aren't enough, borrow 1 hour = 60 minutes.
Tip 3: Always verify by adding elapsed time to start time to get end time.
Tip 4: For AM/PM transitions, break calculation at noon or midnight.
Common Mistakes: Forgetting to carry/borrow, mixing AM/PM, miscalculating minutes over 60.
Memorization Aid: "Start + Elapsed = End" or "End - Start = Elapsed".
Essential Elapsed Time Rules:

• Basic Formula: End Time - Start Time = Elapsed Time

• Find End Time: Start Time + Elapsed Time = End Time

• Find Start Time: End Time - Elapsed Time = Start Time

• Borrowing Rule: 1 hour = 60 minutes

• Carrying Rule: 60 minutes = 1 hour

• AM/PM Rule: 12:00 PM = noon, 12:00 AM = midnight

Important Note: When minutes go over 60, convert to hours. When minutes are insufficient for subtraction, borrow 1 hour = 60 minutes.
Key Strategy: Always check your answer by performing the inverse operation.

Questions & Answers

Question: I get confused when calculating time that goes past noon or midnight. How do I handle AM and PM?

Answer: Great question! Here's how to handle AM and PM transitions:

  • AM: Times from midnight (12:00 AM) to just before noon (11:59 AM)
  • PM: Times from noon (12:00 PM) to just before midnight (11:59 PM)
  • Breaking at noon/midnight: When calculating across these points, break the calculation into segments

Example: From 11:30 AM to 1:15 PM:
• Segment 1: 11:30 AM to 12:00 PM = 30 minutes
• Segment 2: 12:00 PM to 1:15 PM = 1 hour 15 minutes
• Total: 30 min + 1 hr 15 min = 1 hour 45 minutes

Think of noon as a "wall" that separates AM and PM times.

Question: When I subtract times and the minutes in the start time are bigger than the minutes in the end time, what do I do?

Answer: This is called "borrowing" in time calculation! Here's how to do it:

  • When minutes aren't sufficient: Borrow 1 hour from the hours column
  • Convert the borrowed hour: 1 hour = 60 minutes
  • Add to minutes: Add the 60 minutes to the minutes column
  • Subtract 1 from hours: Reduce the hours column by 1

Example: 4:20 PM - 2:45 PM
• Original: 4:20 - 2:45 (can't subtract 45 from 20)
• Borrow: 3:80 - 2:45 (borrowed 1 hour = 60 min, added to 20)
• Calculate: 3-2=1 hour, 80-45=35 minutes
• Answer: 1 hour 35 minutes

This is just like borrowing in regular subtraction, but with 60 instead of 10!

Question: How can I help my child understand elapsed time better? Are there any good visual aids?

Answer: Here are excellent visual strategies for teaching elapsed time:

  1. Number Line: Draw a line and mark start and end times, then count the jumps
  2. Open Number Line: Make jumps of 1 hour, then count remaining minutes
  3. Clock Face: Use a physical or drawn clock to show movement of hands
  4. T-Chart: Organize start time, end time, and elapsed time in columns
  5. Real Objects: Use analog clocks, timers, or schedule activities

Practice with real-life examples: "How long until lunch?" or "What time will dinner be ready?" Make it fun by timing activities like brushing teeth or walking to school. The more they connect elapsed time to their daily routine, the more natural it becomes!

Also, encourage them to "count up" from the start time rather than subtracting when they're first learning.