Solved Exercises on Word Problems with Time Worksheets in Grade 3

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

Solution: Exercises 1 to 3
1 Elapsed time calculation
Exercise 1
A movie started at 6:45 PM and ended at 8:20 PM. How long was the movie?
Definition:

Elapsed time: The difference between two times, calculated by subtracting the start time from the end time

Elapsed time 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
6:45 PM
→
Movie Duration
→
8:20 PM
Step 1: Identify start and end times

Start time: 6:45 PM, End time: 8:20 PM

Step 2: Compare minutes

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

Step 3: Borrow 1 hour from end time

8:20 PM becomes 7:80 PM (since 8:20 = 7:80)

Step 4: Subtract hours and minutes

Hours: 7 - 6 = 1 hour

Minutes: 80 - 45 = 35 minutes

The movie lasted 1 hour and 35 minutes
Final answer:

The movie 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
Sarah started her homework at 4:25 PM. She worked for 1 hour and 55 minutes. What time did she finish?
Definition:

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

4:25 PM
→
+1h 55m
→
6:20 PM
Step 1: Identify start time and duration

Start time: 4:25 PM, Duration: 1 hour 55 minutes

Step 2: Add hours to hours

Hours: 4 + 1 = 5 hours

Step 3: Add minutes to minutes

Minutes: 25 + 55 = 80 minutes

Step 4: Convert excess minutes to hours

80 minutes = 60 + 20 = 1 hour 20 minutes

Step 5: Add converted hours to total

Total hours: 5 + 1 = 6 hours

Total minutes: 20 minutes

Sarah finished at 6:20 PM
Final answer:

Sarah finished her homework at 6:20 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 Time conversion problem
Exercise 3
Emma practiced piano for 2 hours and 35 minutes. How many minutes did she practice in total?
Definition:

Time conversion: Converting mixed time units (hours and minutes) to a single unit (minutes)

2 hours
× 60 = 120 min
35 min
stays same
155 min
total
Step 1: Identify the given time

Emma practiced: 2 hours and 35 minutes

Step 2: Convert hours to minutes

2 hours × 60 minutes/hour = 120 minutes

Step 3: Add the remaining minutes

Total minutes: 120 + 35 = 155 minutes

Step 4: State the final answer

Emma practiced for 155 minutes in total

1 hour = 60 minutes
Total minutes = (hours × 60) + remaining minutes
Emma practiced for 155 minutes
Final answer:

Emma practiced piano for 155 minutes in total

Applied rules:

• Conversion factor: 1 hour = 60 minutes

• Multiplication principle: Multiply hours by 60 to get minutes

• Addition principle: Add converted hours to remaining minutes

Time Calculation 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
Conversion Formula
Total minutes = (H × 60) + M
Convert hours to minutes
Key definitions:

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 conversion: Changing time units from one form to another

Time calculation methods:
  1. Addition: Add hours to hours, minutes to minutes
  2. Subtraction: Subtract hours from hours, minutes from minutes
  3. Conversion: Multiply hours by 60 and add minutes
  4. Elapsed time: End time minus start time
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: Always check if your answer makes sense in the context of the problem.
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 Subtraction with borrowing
Exercise 4
Marcus started reading at 7:15 PM and finished at 8:10 PM. How long did he read?
Definition:

Time subtraction with borrowing: When minutes in start time are greater than minutes in end time, borrow 1 hour (60 minutes)

7:15 PM
→
Reading Time
→
8:10 PM
Step 1: Identify start and end times

Start: 7:15 PM, End: 8:10 PM

Step 2: Compare minutes

Start minutes (15) > End minutes (10), so we need to borrow

Step 3: Borrow 1 hour from end time

8:10 PM becomes 7:70 PM (since 8:10 = 7:70)

Step 4: Subtract hours and minutes

Hours: 7 - 7 = 0 hours

Minutes: 70 - 15 = 55 minutes

Marcus read for 55 minutes
Final answer:

Marcus read for 55 minutes

Applied rules:

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

• Subtraction principle: Subtract hours from hours, minutes from minutes

• Time conversion: 1 hour = 60 minutes for borrowing purposes

5 Multi-step time problem
Exercise 5
Lisa went to school at 8:20 AM. She had lunch at 12:35 PM. Then she went back to class at 1:20 PM and left school at 3:50 PM. How much time did Lisa spend at school in total?
Definition:

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

Morning
8:20 AM - 12:35 PM
Afternoon
1:20 PM - 3:50 PM
Step 1: Break down the problem into parts

Part 1: 8:20 AM to 12:35 PM (morning session)

Part 2: 1:20 PM to 3:50 PM (afternoon session)

Step 2: Calculate morning session

From 8:20 AM to 12:35 PM

Hours: 12 - 8 = 4 hours

Minutes: 35 - 20 = 15 minutes

Morning session: 4 hours 15 minutes

Step 3: Calculate afternoon session

From 1:20 PM to 3:50 PM

Hours: 3 - 1 = 2 hours

Minutes: 50 - 20 = 30 minutes

Afternoon session: 2 hours 30 minutes

Step 4: Add both sessions together

Total hours: 4 + 2 = 6 hours

Total minutes: 15 + 30 = 45 minutes

Since 45 < 60, no conversion needed

Lisa spent 6 hours and 45 minutes at school
Final answer:

Lisa spent 6 hours and 45 minutes at school 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 Concepts and Problem-Solving Strategies

Complete Summary of Time Concepts

Definitions

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 Conversion: Changing time units from one form to another

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 30min + 45min = 4:30 (add sequentially)

Tips & Tricks

Tips: Count by 5s for minutes, draw clocks 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

Additional Practice Problems
Problem A
A soccer match started at 3:15 PM and lasted 1 hour 45 minutes. What time did it end?
Problem B
Tom began studying at 4:30 PM and finished at 6:20 PM. How long did he study?
Problem C
Sarah watched TV for 2 hours 25 minutes. How many minutes is that?
Problem D
A movie lasted from 7:45 AM to 9:30 AM. How long was the movie?
Practice Areas
Elapsed Time
Calculate duration between two times
Time Addition
Find end time by adding duration
Time Subtraction
Find duration by subtracting times
Unit Conversion
Convert between hours and 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. 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