5 Word Problems with Detailed Solutions in Grade 3 Time

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

Problems 1 to 3 with Solutions
1 Elapsed Time
Problem 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

Solution Method:
  1. Identify start time (6:45 PM) and end time (8:20 PM)
  2. Compare minutes: 45 > 20, so we need to borrow
  3. Borrow 1 hour from end time: 8:20 PM becomes 7:80 PM
  4. Subtract hours: 7 - 6 = 1 hour
  5. Subtract minutes: 80 - 45 = 35 minutes
6:45 PM
→
Movie Duration
→
8:20 PM
Step-by-step calculation:

Start time: 6:45 PM

End time: 8:20 PM

Since 45 > 20, we borrow: 8:20 PM = 7:80 PM

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

Key Rules Applied:

• 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 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-by-step calculation:

Start time: 4:25 PM

Duration: 1 hour 55 minutes

Minutes: 25 + 55 = 80 minutes

Convert: 80 minutes = 1 hour 20 minutes

Hours: 4 + 1 (from start) + 1 (converted) = 6 hours

Final time: 6:20 PM

Sarah finished at 6:20 PM
Final Answer:

Sarah finished her homework at 6:20 PM

Key Rules Applied:

• 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 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-by-step calculation:

Given time: 2 hours 35 minutes

Convert hours to minutes: 2 × 60 = 120 minutes

Add remaining minutes: 120 + 35 = 155 minutes

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

Key Rules Applied:

• 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

Problems 4 to 5 with Solutions
4 Time Subtraction
Problem 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-by-step calculation:

Start time: 7:15 PM

End time: 8:10 PM

Since 15 > 10, we borrow: 8:10 PM = 7:70 PM

Hours: 7 - 7 = 0 hours

Minutes: 70 - 15 = 55 minutes

Marcus read for 55 minutes
Final Answer:

Marcus read for 55 minutes

Key Rules Applied:

• 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 Problem
Problem 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-by-step calculation:

Morning session: 8:20 AM to 12:35 PM

Hours: 12 - 8 = 4 hours

Minutes: 35 - 20 = 15 minutes

Morning: 4 hours 15 minutes

Afternoon session: 1:20 PM to 3:50 PM

Hours: 3 - 1 = 2 hours

Minutes: 50 - 20 = 30 minutes

Afternoon: 2 hours 30 minutes

Total: 4h 15m + 2h 30m = 6 hours 45 minutes

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

Lisa spent 6 hours and 45 minutes at school in total

Key Rules Applied:

• Problem decomposition: Break complex problems into smaller parts

• Sequential calculation: Calculate each part separately

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

Comprehensive 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

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