Solved Exercises on Word Problems with Time Intervals in Grade 3

Master time intervals: elapsed time, duration, scheduling, and practical applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Elapsed time calculation
Exercise 1
A basketball game started at 3:45 PM and ended at 5:20 PM. How long was the game?
Definition:

Time interval: The duration between two specific times, calculated by subtracting the start time from the end time

Time interval method:
  1. Identify the start and end times
  2. Subtract hours from hours
  3. Subtract minutes from minutes
  4. If minutes insufficient, borrow 1 hour
3:45 PM
→
Game Duration
→
5:20 PM
Step 1: Identify start and end times

Start time: 3:45 PM, End time: 5:20 PM

Step 2: Compare minutes

Start minutes (45) > End minutes (20), so we need to borrow

Step 3: Borrow 1 hour from end time

5:20 PM becomes 4:80 PM (since 5:20 = 4:80)

Step 4: Subtract hours and minutes

Hours: 4 - 3 = 1 hour

Minutes: 80 - 45 = 35 minutes

The game lasted 1 hour and 35 minutes
Final answer:

The basketball game lasted 1 hour and 35 minutes

Applied rules:

• Subtraction principle: End time - Start time

• Borrowing rule: When minutes insufficient, borrow 1 hour (add 60 minutes)

• Time calculation: Subtract hours from hours, minutes from minutes

2 Time addition problem
Exercise 2
Maria started her piano lesson at 4:30 PM. The lesson lasted 1 hour and 45 minutes. What time did it end?
Definition:

Time addition: Adding a duration to a start time to find an end time

4:30 PM
→
+1h 45m
→
6:15 PM
Step 1: Identify start time and duration

Start time: 4:30 PM, Duration: 1 hour 45 minutes

Step 2: Add hours to hours

Hours: 4 + 1 = 5 hours

Step 3: Add minutes to minutes

Minutes: 30 + 45 = 75 minutes

Step 4: Convert excess minutes to hours

75 minutes = 60 + 15 = 1 hour 15 minutes

Step 5: Add converted hours to total

Total hours: 5 + 1 = 6 hours

Total minutes: 15 minutes

The lesson ended at 6:15 PM
Final answer:

Maria's piano lesson ended at 6:15 PM

Applied rules:

• Time addition: Add hours to hours, minutes to minutes

• Conversion rule: When minutes ≥ 60, convert to hours

• Carry over: 60 minutes = 1 hour

3 Multiple time intervals
Exercise 3
John played soccer for 45 minutes, then studied for 1 hour and 30 minutes, and finally practiced piano for 20 minutes. How much total time did John spend on activities?
Definition:

Multiple time intervals: Adding several time durations together to find a total time

Soccer
45 min
Study
1h 30m
Piano
20 min
Step 1: List all time intervals

Soccer: 45 minutes

Study: 1 hour 30 minutes

Piano: 20 minutes

Step 2: Add all hours together

Total hours: 0 + 1 + 0 = 1 hour

Step 3: Add all minutes together

Total minutes: 45 + 30 + 20 = 95 minutes

Step 4: Convert excess minutes to hours

95 minutes = 60 + 35 = 1 hour 35 minutes

Step 5: Combine hours and minutes

Total time: 1 hour + 1 hour 35 minutes = 2 hours 35 minutes

John spent 2 hours and 35 minutes on activities
Final answer:

John spent 2 hours and 35 minutes on activities

Applied rules:

• Grouping principle: Add hours together, add minutes together

• Conversion rule: When minutes ≥ 60, convert to hours

• Time addition: Combine all time intervals

Time Interval Fundamentals
1 \text{ hour} = 60 \text{ minutes}
Basic Time Conversion
Time Addition
H₁ + H₂, M₁ + M₂
If M₁ + M₂ ≥ 60, convert to hours
Time Subtraction
H₂ - H₁, M₂ - M₁
If M₁ > M₂, borrow 1 hour
Interval Formula
End Time - Start Time
Find the duration
Key definitions:

Time interval: The duration between two specific times

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

Duration: The length of time something takes

Start time: When an event begins

End time: When an event finishes

Time interval methods:
  1. Subtraction: End time - Start time (for finding duration)
  2. Addition: Start time + Duration (for finding end time)
  3. Conversion: Convert mixed units to single unit
  4. Grouping: Add multiple intervals together
Tip 1: When adding minutes, if the sum is 60 or more, convert 60 minutes to 1 hour.
Tip 2: When subtracting minutes and the start minutes are greater, borrow 1 hour (60 minutes) from the hours.
Tip 3: Draw a timeline to visualize the problem when it gets complex.
Common errors: Forgetting to convert minutes to hours when adding, not borrowing correctly when subtracting, misreading clock faces.
Key relationships: 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day.
Important time facts to remember:

• 1 hour = 60 minutes

• 1 minute = 60 seconds

• 24 hours = 1 day

• When adding: If minutes ≥ 60, convert to hours

• When subtracting: If minutes insufficient, borrow 1 hour

Solution: Exercises 4 to 5
4 Time interval with breaks
Exercise 4
A movie started at 2:15 PM. It lasted 1 hour and 45 minutes with a 15-minute intermission. What time did the movie end?
Definition:

Time interval with breaks: Calculating total time including both activity time and break time

2:15
Start
4:00
End
Step 1: Identify start time and components

Start time: 2:15 PM

Movie duration: 1 hour 45 minutes

Intermission: 15 minutes

Step 2: Calculate total duration

Total time: 1 hour 45 minutes + 15 minutes = 1 hour 60 minutes

Convert: 1 hour 60 minutes = 2 hours 0 minutes

Step 3: Add total duration to start time

2:15 PM + 2 hours = 4:15 PM

The movie ended at 4:15 PM
Final answer:

The movie ended at 4:15 PM

Applied rules:

• Addition principle: Add all time components together

• Conversion rule: 60 minutes = 1 hour

• Time calculation: Add total duration to start time

5 Multi-step time interval problem
Exercise 5
Emma left home at 8:30 AM. She walked to school for 20 minutes, attended class from 9:00 AM to 12:15 PM, had lunch for 45 minutes, then attended afternoon class until 3:30 PM. How long was Emma at school in total?
Definition:

Multi-step time interval problem: Calculating multiple time intervals and summing them to find total duration

Walking
20 min
Morning
3h 15m
Lunch
45 min
Afternoon
2h 15m
Step 1: Break down the problem into parts

Walking to school: 20 minutes

Morning class: 9:00 AM to 12:15 PM = 3 hours 15 minutes

Lunch: 45 minutes

Afternoon class: 12:15 PM to 3:30 PM = 3 hours 15 minutes

Step 2: Calculate morning class duration

From 9:00 AM to 12:15 PM

Hours: 12 - 9 = 3 hours

Minutes: 15 - 0 = 15 minutes

Morning class: 3 hours 15 minutes

Step 3: Calculate afternoon class duration

From 12:15 PM to 3:30 PM

Hours: 3 - 12 = 3 hours (12:15 PM to 3:15 PM = 3 hours)

Plus 15 more minutes to 3:30 PM

Afternoon class: 3 hours 15 minutes

Step 4: Sum all time intervals

Walking: 20 minutes

Morning class: 3 hours 15 minutes

Lunch: 45 minutes

Afternoon class: 3 hours 15 minutes

Step 5: Add all components together

Hours: 0 + 3 + 0 + 3 = 6 hours

Minutes: 20 + 15 + 45 + 15 = 95 minutes

Convert: 95 minutes = 1 hour 35 minutes

Total: 6 hours + 1 hour 35 minutes = 7 hours 35 minutes

Emma was at school for 7 hours and 35 minutes
Final answer:

Emma was at school for 7 hours and 35 minutes in total

Applied rules:

• Problem decomposition: Break complex problems into smaller parts

• Sequential calculation: Calculate each part separately

• Time addition: Add hours to hours, minutes to minutes

Detailed Summary: Time Interval Concepts and Problem-Solving Strategies

Complete Summary of Time Interval Concepts

Definitions

Time Interval: The duration between two specific times

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

Duration: The length of time something takes

Start Time: When an event begins

End Time: When an event finishes

Core Rules

Time Conversion: 1 hour = 60 minutes, 1 minute = 60 seconds

Carry Over Rule: When minutes ≥ 60, convert to hours

Borrowing Rule: When subtracting and minutes insufficient, borrow 1 hour = 60 minutes

Time Addition: Add hours to hours, minutes to minutes

Time Subtraction: Subtract hours from hours, minutes from minutes

Problem-Solving Steps

Step 1: Read the problem carefully and identify what's being asked

Step 2: Identify given times (start, end, duration)

Step 3: Determine operation needed (addition or subtraction)

Step 4: Perform calculations step by step

Step 5: Check if answer makes sense in context

Examples

Simple: 3:15 + 45 min = 4:00 (15+45=60, carry over 1 hour)

Intermediate: 4:30 + 2 hours 45 min = 7:15 (carry over 1 hour from 75 minutes)

Advanced: 5:20 - 1 hour 40 min = 3:40 (borrow 1 hour: 4:80 - 1:40)

Multi-step: 2:15 + 1h 30m + 45m = 4:30 (add sequentially)

Tips & Tricks

Tips: Count by 5s for minutes, draw timelines for visualization, check answers by working backwards

Common Mistakes: Forgetting to carry over, misreading hour hand, incorrect minute counting

Pitfalls: Confusing hour and minute hands, not borrowing when subtracting

Memorization Aids

Memory: "If minutes reach 60, make one more hour"

Pattern: Numbers on clock face: 1→5, 2→10, 3→15, 4→20, 6→30, 9→45, 12→0

Key Points: Hour hand moves slowly, minute hand moves quickly

Formula: Total minutes = (hours × 60) + minutes

Questions & Answers

Question: I don't understand when I need to borrow minutes when subtracting time. Can you explain when this happens?

Answer: You need to borrow when the minutes in the start time are greater than the minutes in the end time. Think of it like regular subtraction:

  • If you have 4:15 PM - 2:30 PM, since 15 < 30, you need to borrow
  • You borrow 1 hour from 4:15 PM, which becomes 3:75 PM (since 1 hour = 60 minutes, 15 + 60 = 75)
  • Now you can subtract: 3:75 PM - 2:30 PM = 1:45 PM

This is just like borrowing in regular math: if you have 42 - 17, you borrow from the tens place. With time, you borrow from the hour place.

Example: 5:20 PM - 2:45 PM → Since 20 < 45, borrow 1 hour: 4:80 PM - 2:45 PM = 2:35 PM

Question: When I add time and get more than 60 minutes, how do I convert that to hours and minutes?

Answer: When minutes add up to 60 or more, divide by 60 to find how many full hours you have:

  • Every 60 minutes equals 1 hour
  • Take the whole number of hours from dividing by 60
  • The remainder is the extra minutes

Example: If you get 95 minutes after adding:

95 ÷ 60 = 1 remainder 35

So 95 minutes = 1 hour and 35 minutes

Another example: 140 minutes = 140 ÷ 60 = 2 remainder 20 = 2 hours and 20 minutes

Always remember: 60 minutes = 1 hour, 120 minutes = 2 hours, 180 minutes = 3 hours, etc.

Question: I have trouble with word problems about time intervals. How do I know whether to add or subtract?

Answer: Look for key words and phrases in the problem:

  • Add when: "How long did it take?", "What time did it finish?", "Total time", "Combined time", "added to"
  • Subtract when: "How long was it?", "How much longer?", "elapsed time", "difference", "how much time passed"

Also consider the context:

  • If you know start time and duration → Add to find end time
  • If you know start and end time → Subtract to find duration
  • If you know end time and duration → Subtract to find start time

Example: "Started at 2 PM, worked 3 hours → What time did it finish?" → Add: 2 PM + 3 hours = 5 PM

Example: "Started at 2 PM, finished at 5 PM → How long?" → Subtract: 5 PM - 2 PM = 3 hours