Solved Exercises on Elapsed Time Within the Hour in Grade 3

Master elapsed time calculations: time intervals, word problems, clock reading, and time management through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic elapsed time calculation
Exercise 1
Sarah started her homework at 2:15 PM and finished at 2:45 PM. How much time did she spend on her homework?
Definition:

Elapsed time: The amount of time that passes between two specific times. It's calculated by subtracting the start time from the end time.

Elapsed time method:
  1. Identify the start time (2:15 PM)
  2. Identify the end time (2:45 PM)
  3. Subtract minutes: End minutes - Start minutes
  4. If necessary, convert hours to minutes for easier calculation
Start Time
2:15 PM
End Time
2:45 PM
Elapsed Time
30 minutes
Step 1: Identify start and end times

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

Step 2: Calculate the difference in minutes

From 2:15 PM to 2:45 PM, count the minutes: 15, 16, 17, ..., 45 = 30 minutes

Step 3: Alternative calculation method

45 minutes - 15 minutes = 30 minutes

Sarah spent 30 minutes on her homework.
Final answer:

Sarah spent 30 minutes on her homework.

Applied rules:

• Elapsed time rule: End time - Start time = Elapsed time

• Minute calculation: Count minutes within the same hour

• Time conversion: Hours can be converted to minutes for easier calculation

Tip: When both times are in the same hour, just subtract the minutes.
Common mistake: Don't subtract hours and minutes separately without considering the relationship.
⏰ Clock Face
Start: 2:15
End: 2:45
Elapsed: 30 min
2 Time interval problem
Exercise 2
A movie started at 3:20 PM and ended at 4:05 PM. How long was the movie?
Definition:

Time interval: The duration between two times that may cross over to the next hour. When crossing an hour boundary, break the calculation into segments.

Start Time
3:20 PM
End Time
4:05 PM
Elapsed Time
45 minutes
Step 1: Break the calculation into segments

From 3:20 PM to 4:00 PM = 40 minutes

From 4:00 PM to 4:05 PM = 5 minutes

Step 2: Add the segments together

40 minutes + 5 minutes = 45 minutes

Step 3: Alternative method using total minutes

3:20 PM = 3×60 + 20 = 200 minutes from midnight

4:05 PM = 4×60 + 5 = 245 minutes from midnight

245 - 200 = 45 minutes

The movie lasted 45 minutes.
Final answer:

The movie lasted 45 minutes.

Applied rules:

• Cross-hour calculation: When crossing an hour, calculate in segments

• Segmentation method: Break into parts that don't cross hours

• Total minute conversion: Convert both times to minutes and subtract

Tip: When crossing an hour, go to the next full hour first, then add the remaining minutes.
Common mistake: Don't subtract minutes directly when hours change (e.g., 4:05 - 3:20 ≠ 85 minutes).
⏰ Clock Face
Start: 3:20
End: 4:05
Crossed hour
Elapsed: 45 min
3 Word problem with elapsed time
Exercise 3
Emma started reading at 1:10 PM. She read for 35 minutes. What time did she finish reading?
Definition:

Time calculation forward: Adding elapsed time to a start time to find an end time. This involves adding minutes and potentially carrying over to the next hour.

Start Time
1:10 PM
Duration
35 minutes
End Time
1:45 PM
Step 1: Identify the start time and duration

Start: 1:10 PM, Duration: 35 minutes

Step 2: Add the minutes to the start time

1:10 PM + 35 minutes = 1:(10+35) PM = 1:45 PM

Step 3: Check if minutes exceed 60

Since 10 + 35 = 45 (less than 60), no hour carryover needed

Emma finished reading at 1:45 PM.
Final answer:

Emma finished reading at 1:45 PM.

Applied rules:

• Addition rule: Start time + Duration = End time

• Carryover rule: If minutes ≥ 60, add 1 hour and subtract 60 minutes

• Hour boundary: Crossing 60 minutes moves to next hour

Tip: When adding minutes, if the total exceeds 60, add 1 to the hour and subtract 60 from minutes.
Common mistake: Don't forget to carry over when minutes reach 60 or more.
⏰ Clock Face
Start: 1:10
Added: 35 min
End: 1:45
Rules and methods, laws,...
Elapsed Time = End Time - Start Time
Basic Elapsed Time Formula
Rule 1
Same Hour
Minutes Only Subtraction
Rule 2
Cross Hour
Segment Calculation
Rule 3
Time Forward
Add Minutes Method
Key definitions:

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

Start time: The time when an activity begins

End time: The time when an activity ends

Duration: The length of time an activity takes

Complete methodology:
  1. Identify the problem: Determine if finding elapsed time, start time, or end time
  2. Extract information: Find start time, end time, or duration given
  3. Choose method: Same hour subtraction, cross-hour segmentation, or time addition
  4. Calculate: Perform the time arithmetic
  5. Verify: Check if answer makes sense in context
Key facts: There are 60 minutes in 1 hour, 24 hours in 1 day.
Time format: Hours (0-12) with minutes (00-59) and AM/PM indicators.
Solution: Exercises 4 to 5
4 Multi-step elapsed time
Exercise 4
Tom started jogging at 6:30 AM. He jogged for 25 minutes, took a 10-minute break, and then jogged for another 15 minutes. What time did he finish?
Definition:

Multi-step time calculation: Problems involving multiple activities with different durations that must be added sequentially to the start time.

Start Time
6:30 AM
Total Duration
25+10+15=50 min
End Time
7:20 AM
Step 1: List all time segments

Jogging: 25 minutes

Break: 10 minutes

Jogging: 15 minutes

Step 2: Calculate total duration

25 + 10 + 15 = 50 minutes

Step 3: Add total duration to start time

6:30 AM + 50 minutes = 6:(30+50) AM = 6:80 AM

Since 80 > 60, convert: 6:80 AM = 7:20 AM

Tom finished at 7:20 AM.
Final answer:

Tom finished at 7:20 AM.

Applied rules:

• Sequential addition: Add all time segments together

• Carryover rule: When minutes ≥ 60, add 1 hour and subtract 60 minutes

• Order matters: Add time segments in chronological order

Tip: Add up all the time segments first, then add to the start time.
Common mistake: Don't forget to handle the hour carryover when minutes exceed 60.
⏰ Clock Face
Start: 6:30
Total: 50 min
End: 7:20
5 Finding start time
Exercise 5
A soccer game lasted 90 minutes and ended at 4:15 PM. What time did the game start?
Definition:

Finding start time: When given the end time and duration, subtract the duration from the end time to find the start time.

End Time
4:15 PM
Duration
90 minutes
Start Time
2:45 PM
Step 1: Identify known values

End time: 4:15 PM, Duration: 90 minutes

Step 2: Convert duration to hours and minutes

90 minutes = 1 hour and 30 minutes

Step 3: Subtract from end time

4:15 PM - 1 hour = 3:15 PM

3:15 PM - 30 minutes = 2:45 PM

Step 4: Alternative method

Convert to total minutes: 4:15 PM = 4×60+15 = 255 minutes

255 - 90 = 165 minutes

165 ÷ 60 = 2 hours with remainder 45 minutes → 2:45 PM

The game started at 2:45 PM.
Final answer:

The game started at 2:45 PM.

Applied rules:

• Start time rule: End time - Duration = Start time

• Backward calculation: Subtract time going backwards

• Borrowing rule: If minutes go negative, borrow 1 hour (60 minutes)

Tip: When subtracting and minutes go negative, borrow 1 hour (60 minutes) from the hour.
Common mistake: Don't subtract hours and minutes separately without borrowing when needed.
⏰ Clock Face
End: 4:15
Duration: 90 min
Start: 2:45
Complete Guide to Elapsed Time Rules and Methods
Elapsed Time = End Time - Start Time
Elapsed Time Formula
Key definitions:

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

Start time: The time when an activity begins

End time: The time when an activity ends

Duration: The length of time an activity takes

AM: Ante meridiem (before noon, 12:00 AM to 11:59 AM)

PM: Post meridiem (after noon, 12:00 PM to 11:59 PM)

Complete methodology:
  1. Identify the problem: Determine if finding elapsed time, start time, or end time
  2. Extract information: Find start time, end time, or duration given
  3. Choose method: Same hour subtraction, cross-hour segmentation, or time addition
  4. Calculate: Perform the time arithmetic
  5. Verify: Check if answer makes sense in context
Tip 1: When both times are in the same hour, just subtract the minutes.
Tip 2: When crossing an hour, break the calculation into segments.
Tip 3: If minutes exceed 60 when adding, carry over to the next hour.
Tip 4: If minutes go negative when subtracting, borrow from the hour.
Common errors: Forgetting to carry over when minutes reach 60, subtracting in wrong order, misreading clock positions.
Exam preparation: Practice with different time formats, work on word problems, understand AM/PM differences.
Essential formulas to remember:

• Elapsed Time = End Time - Start Time

• End Time = Start Time + Duration

• Start Time = End Time - Duration

• 1 hour = 60 minutes

• When minutes ≥ 60, add 1 hour and subtract 60 minutes

• When minutes < 0, subtract 1 hour and add 60 minutes

Questions & Answers

Question: My students struggle with elapsed time problems where the time crosses an hour boundary. How can I help them visualize this better?

Answer: Great question! Here are effective strategies for teaching cross-hour elapsed time:

  • Use a number line approach: Draw a number line showing the full hour (e.g., 3:00 to 4:00) and mark the start and end times
  • Break it into segments: Go to the next full hour first, then add the remaining minutes
  • Use visual aids like analog clocks to show the movement of hands

For example, with 3:45 to 4:20:
Step 1: 3:45 to 4:00 = 15 minutes
Step 2: 4:00 to 4:20 = 20 minutes
Total: 15 + 20 = 35 minutes

This segment approach makes it concrete and easier to understand.

Question: I get confused when I need to subtract minutes and they go below zero. Like if I need to subtract 20 minutes from 3:05. What should I do?

Answer: That's a great question! When minutes go below zero, you need to "borrow" from the hour:

  • Take 1 hour from the hour part (3:05 becomes 2:65)
  • Add 60 minutes to the minutes part (05 + 60 = 65)
  • Now subtract: 2:65 - 0:20 = 2:45

Think of it like money: if you have $3.05 and spend $0.20, but you think of it as $2.65 (since $3.05 = $2.65), then $2.65 - $0.20 = $2.45.

So 3:05 - 20 minutes = 2:45. The hour goes down by 1, and the minutes go up by 60.

Question: How can I make elapsed time problems more engaging for my child who loves stories?

Answer: Storytelling is excellent for learning! Try these approaches:

  • Create character-based scenarios: "Captain Time needs to know how long his treasure hunt lasted..."
  • Use real-life contexts: sports games, cooking times, school schedules
  • Make it a mystery: "What time did the party start if it ended at 3:30 and lasted 2 hours?"
  • Use time travel themes: "If the time machine left at 11:45 and returned after 45 minutes, when did it return?"

Example story problem: "Princess Elapsed started her royal duties at 9:15 AM. She had breakfast for 20 minutes, then attended a meeting for 35 minutes. What time did her meeting end?"

Stories make abstract concepts concrete and memorable!