Solved Exercises on Word Problems Involving Hours and Minutes in Grade 3

Master time calculations: addition, subtraction, elapsed time, conversion, and practical applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Addition of time
Exercise 1
Sarah started her homework at 3:45 PM. She worked for 1 hour and 30 minutes. What time did she finish?
Definition:

Addition of time: Adding hours and minutes separately, converting minutes to hours when necessary

Time addition method:
  1. Add the hours together
  2. Add the minutes together
  3. If minutes ≥ 60, convert to hours (divide by 60)
  4. Add converted hours to total hours
3:45 PM
→
+1h 30m
→
5:15 PM
Step 1: Identify starting time and duration

Starting time: 3:45 PM, Duration: 1 hour 30 minutes

Step 2: Add hours to hours

Hours: 3 + 1 = 4 hours

Step 3: Add minutes to minutes

Minutes: 45 + 30 = 75 minutes

Step 4: Convert excess minutes to hours

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

Step 5: Add converted hours to total

Total hours: 4 + 1 = 5 hours

Total minutes: 15 minutes

Sarah finished at 5:15 PM
Final answer:

Sarah finished her homework at 5:15 PM

Applied rules:

• Time conversion: 60 minutes = 1 hour

• Addition principle: Add hours to hours, minutes to minutes

• Carry over: When minutes ≥ 60, convert to hours

2 Elapsed time
Exercise 2
A movie started at 2:30 PM and ended at 4:45 PM. How long was the movie?
Definition:

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

2:30 PM
→
Movie Duration
→
4:45 PM
Step 1: Identify start and end times

Start time: 2:30 PM, End time: 4:45 PM

Step 2: Subtract hours

Hours: 4 - 2 = 2 hours

Step 3: Subtract minutes

Minutes: 45 - 30 = 15 minutes

Step 4: Combine results

Elapsed time: 2 hours 15 minutes

The movie lasted 2 hours and 15 minutes
Final answer:

The movie lasted 2 hours and 15 minutes

Applied rules:

• Subtraction principle: End time - Start time

• Borrowing rule: If minutes in start time > minutes in end time, borrow 1 hour (60 minutes)

• Time calculation: Subtract hours separately, then minutes separately

3 Conversion of time units
Exercise 3
Emma practiced piano for 2 hours and 45 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
45 min
stays same
165 min
total
Step 1: Identify the given time

Emma practiced: 2 hours and 45 minutes

Step 2: Convert hours to minutes

2 hours × 60 minutes/hour = 120 minutes

Step 3: Add the remaining minutes

Total minutes: 120 + 45 = 165 minutes

Step 4: State the final answer

Emma practiced for 165 minutes in total

1 hour = 60 minutes
Total minutes = (hours × 60) + remaining minutes
Emma practiced for 165 minutes
Final answer:

Emma practiced piano for 165 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 Conversion & Key Concepts
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 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 6:20 PM and finished at 7:10 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)

6:20 PM
→
Reading Time
→
7:10 PM
Step 1: Identify start and end times

Start: 6:20 PM, End: 7:10 PM

Step 2: Compare minutes

Start minutes (20) > End minutes (10), so we need to borrow

Step 3: Borrow 1 hour from end time

7:10 PM becomes 6:70 PM (since 1 hour = 60 minutes)

Step 4: Subtract hours and minutes

Hours: 6 - 6 = 0 hours

Minutes: 70 - 20 = 50 minutes

Marcus read for 50 minutes
Final answer:

Marcus read for 50 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 8:15 AM. She had lunch at 12:30 PM. Then she went back to class at 1:15 PM and left school at 3:45 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
8:15 AM - 12:30 PM
Afternoon
1:15 PM - 3:45 PM
Step 1: Break down the problem into parts

Part 1: 8:15 AM to 12:30 PM (morning session)

Part 2: 1:15 PM to 3:45 PM (afternoon session)

Step 2: Calculate morning session

From 8:15 AM to 12:30 PM

Hours: 12 - 8 = 4 hours

Minutes: 30 - 15 = 15 minutes

Morning session: 4 hours 15 minutes

Step 3: Calculate afternoon session

From 1:15 PM to 3:45 PM

Hours: 3 - 1 = 2 hours

Minutes: 45 - 15 = 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

Time Calculation Fundamentals & Problem-Solving Strategies
1 \text{ hour} = 60 \text{ minutes}
Time Conversion
Key definitions:

Elapsed time: The difference between two times

Duration: The length of time an activity takes

Time conversion: Changing time units from one form to another

Time addition: Combining hours and minutes with proper conversions

Complete time problem-solving methodology:
  1. Read the problem carefully: Identify start time, end time, or duration
  2. Identify what to find: Is it elapsed time, end time, or start time?
  3. Plan the approach: Choose addition, subtraction, or conversion method
  4. Calculate step by step: Work with hours and minutes separately
  5. Check the answer: Does it make sense in the context?
Tip 1: Draw a timeline to visualize the problem when it gets complex.
Tip 2: When subtracting time and minutes are insufficient, borrow 1 hour (60 minutes).
Tip 3: Always verify your answer by adding the result back to the start time.
Tip 4: Practice with real-life scenarios like school schedules, TV programs, or travel times.
Common errors: Forgetting to convert when minutes ≥ 60, incorrect borrowing, misreading analog clocks.
Exam preparation: Practice word problems, memorize time conversions, master borrowing technique.
Time calculation rules to remember:

• Conversion: 1 hour = 60 minutes

• Addition: Add hours to hours, minutes to minutes

• Carry over: If minutes ≥ 60, convert to hours

• Subtraction: Subtract hours from hours, minutes from minutes

• Borrowing: If minutes insufficient, borrow 1 hour = 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. 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