Solved Exercises on Time Word Problems in Grade 8

Master time calculations: elapsed time, time conversions, and time word problems through these 5 detailed exercises with comprehensive methods and tips.

Solution: Exercises 1 to 3
1 Elapsed Time Calculation
Exercise 1
Sarah started her homework at 3:45 PM and finished at 5:20 PM. How much time did she spend on her homework?
Definition:

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

Time calculation method:
  1. Identify the start and end times
  2. Calculate hours first, then minutes
  3. If minutes in start time > minutes in end time, borrow an hour
  4. Combine hours and minutes for total elapsed time
Start Time
3:45 PM
End Time
5:20 PM
Step 1: Identify start and end times

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

Step 2: Calculate hours and minutes separately

Hours: 5 - 3 = 2 hours

Minutes: 20 - 45 = ? Since 20 < 45, we need to borrow

Step 3: Borrow an hour to subtract minutes

Convert 1 hour to 60 minutes: 2 hours - 1 hour = 1 hour

Add to minutes: 20 + 60 = 80 minutes

Now subtract: 80 - 45 = 35 minutes

Step 4: Combine hours and minutes

Total time = 1 hour 35 minutes

Sarah spent 1 hour and 35 minutes on her homework
Final answer:

Sarah spent 1 hour and 35 minutes on her homework

Applied rules:

• Elapsed time: End time - Start time

• Borrowing rule: When minutes in start > minutes in end, borrow 1 hour = 60 minutes

• Time conversion: 1 hour = 60 minutes

2 Time Conversion Problem
Exercise 2
A movie lasted 2 hours and 45 minutes. Express this duration in minutes only.
Definition:

Time conversion: Changing time from one unit to another (hours to minutes, etc.).

Hours
2
Minutes
45
Unit Conversion Factor Value
Hours to Minutes × 60 2 × 60 = 120 minutes
Additional Minutes No conversion needed 45 minutes
Step 1: Convert hours to minutes

2 hours = 2 × 60 = 120 minutes

Step 2: Add the additional minutes

120 minutes + 45 minutes = 165 minutes

Step 3: State the final answer

The movie lasted 165 minutes

The movie lasted 165 minutes
Final answer:

The movie lasted 165 minutes

Applied rules:

• Time conversion: 1 hour = 60 minutes

• Multiplication: Hours × 60 = minutes

• Addition: Total minutes = converted hours + original minutes

3 Multi-day Time Problem
Exercise 3
A train departed on Monday at 9:30 AM and arrived at its destination on Wednesday at 2:15 PM. How long was the journey?
Definition:

Multi-day elapsed time: Time that spans across multiple days, requiring day counting.

Departure
Mon 9:30 AM
Arrival
Wed 2:15 PM
Step 1: Count full days

From Monday 9:30 AM to Tuesday 9:30 AM = 24 hours

From Tuesday 9:30 AM to Wednesday 9:30 AM = 24 hours

Full days = 48 hours

Step 2: Calculate remaining time from 9:30 AM to 2:15 PM on Wednesday

From 9:30 AM to 12:00 PM = 2 hours 30 minutes

From 12:00 PM to 2:15 PM = 2 hours 15 minutes

Total = 2 hours 30 minutes + 2 hours 15 minutes = 4 hours 45 minutes

Step 3: Add full days and remaining time

48 hours + 4 hours 45 minutes = 52 hours 45 minutes

Step 4: Convert to days and hours (optional)

52 hours = 2 days and 4 hours

Total = 2 days 4 hours 45 minutes

The journey lasted 52 hours and 45 minutes (or 2 days 4 hours 45 minutes)
Final answer:

The journey lasted 52 hours and 45 minutes

Applied rules:

• Day counting: Full days = number of complete 24-hour periods

• Partial day calculation: Calculate time within the same day

• Time addition: Add full days and partial day time

Time Conversion Rules and Methods
1 hour = 60 minutes
Basic Time Conversion
Time Units
1 minute = 60 seconds
Seconds to Minutes
Time Units
1 hour = 60 minutes
Minutes to Hours
Time Units
1 day = 24 hours
Hours to Days
Key definitions:

Elapsed time: The difference between two times

Time conversion: Changing time from one unit to another

Time word problems: Real-world problems involving time calculations

Complete methodology:
  1. Read carefully: Identify start time, end time, and what is being asked
  2. Plan: Decide whether to calculate hours first or convert to common units
  3. Execute: Perform calculations with attention to borrowing/adding
  4. Verify: Check if the answer makes sense in context
Tip 1: Draw a timeline to visualize the problem.
Tip 2: When minutes in start > minutes in end, always borrow 1 hour (60 minutes).
Tip 3: For multi-day problems, count full days first, then calculate partial days.
Tip 4: Always check if your answer is reasonable.
Common errors: Forgetting to borrow when minutes exceed, mixing up AM/PM, incorrect conversion factors.
Key facts: Remember basic time conversions: 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day.
Time conversion formulas:

• Hours to minutes: multiply by 60

• Minutes to hours: divide by 60

• Days to hours: multiply by 24

• Hours to days: divide by 24

• Elapsed time: End time - Start time

Solution: Exercises 4 to 5
4 Complex Time Addition
Exercise 4
Emma practiced piano for 1 hour 45 minutes on Monday, 2 hours 20 minutes on Tuesday, and 1 hour 35 minutes on Wednesday. What is her total practice time?
Definition:

Time addition: Adding multiple time durations together.

Monday
1:45
Tuesday
2:20
Wednesday
1:35
Step 1: Add hours separately

1 hour + 2 hours + 1 hour = 4 hours

Step 2: Add minutes separately

45 minutes + 20 minutes + 35 minutes = 100 minutes

Step 3: Convert excess minutes to hours

Since 100 minutes > 60 minutes, convert to hours:

100 ÷ 60 = 1 hour with remainder 40 minutes

Step 4: Combine hours

Total hours = 4 hours + 1 hour = 5 hours

Total minutes = 40 minutes

Emma's total practice time was 5 hours and 40 minutes
Final answer:

Emma's total practice time was 5 hours and 40 minutes

Applied rules:

• Time addition: Add hours and minutes separately

• Conversion: When minutes ≥ 60, convert to hours

• Regrouping: Add converted hours to total hours

5 Time Subtraction with Borrowing
Exercise 5
A flight was scheduled to depart at 10:15 AM but was delayed by 2 hours and 50 minutes. What was the actual departure time?
Definition:

Time addition with delay: Adding delay time to original time.

Scheduled Time
10:15 AM
Delay
2:50
Step 1: Add hours to scheduled time

10:15 AM + 2 hours = 12:15 PM

Step 2: Add the remaining minutes

12:15 PM + 50 minutes = ?

15 + 50 = 65 minutes

Step 3: Convert excess minutes to hours

65 minutes = 1 hour and 5 minutes

So 12:15 PM + 50 minutes = 1:05 PM (next hour)

Step 4: State the final answer

The flight actually departed at 1:05 PM

The flight actually departed at 1:05 PM
Final answer:

The flight actually departed at 1:05 PM

Applied rules:

• Time addition: Add delay to scheduled time

• Carry over: When minutes ≥ 60, add 1 hour

• AM/PM handling: Be careful with transitions across noon/midnight

Time Conversion Laws, Methods, Rules, and Definitions
End Time - Start Time = Elapsed Time
Time Calculation Formula
Key definitions:

Elapsed time: The difference between two specific times

Time conversion: Changing time measurements from one unit to another

Time word problems: Real-life scenarios requiring time calculations

Complete methodology:
  1. Problem identification: Determine what type of time calculation is needed
  2. Unit selection: Choose appropriate time units for calculation
  3. Execution: Perform calculations following time arithmetic rules
  4. Verification: Check answer against problem context
Tip 1: Always write times in the same format (AM/PM or 24-hour).
Tip 2: Use a number line for visualizing time differences.
Tip 3: Break complex problems into smaller parts.
Tip 4: Practice mental math for common time intervals.
Common errors: Misreading analog clocks, forgetting to carry over minutes, adding instead of subtracting for elapsed time.
Exam preparation: Master basic conversions, practice word problems, learn to identify key phrases indicating time operations.
Time conversion formulas to know:

• 1 minute = 60 seconds

• 1 hour = 60 minutes

• 1 day = 24 hours

• 1 week = 7 days

• Elapsed time = End time - Start time

Questions & Answers

Question: I get confused when subtracting times like 3:15 PM - 1:45 PM. Why do I need to borrow? Can you explain the process?

Answer: Great question! You need to borrow because you can't subtract 45 minutes from 15 minutes directly. Here's the systematic approach:

  • You have: 3:15 PM - 1:45 PM
  • Minutes: 15 - 45 = ? Since 15 < 45, you need to borrow
  • Borrow 1 hour from 3 hours, which equals 60 minutes
  • New time: 2:75 PM (3 hours - 1 hour = 2 hours, 15 minutes + 60 minutes = 75 minutes)
  • Now subtract: 2:75 PM - 1:45 PM = 1:30 PM

The key insight is that borrowing 1 hour gives you 60 extra minutes, just like borrowing in regular subtraction. This makes the minutes subtraction possible.

Question: How do I handle time problems that cross over midnight, like calculating sleep time from 11:30 PM to 7:15 AM?

Answer: When time crosses midnight, break the problem into two parts:

  • From 11:30 PM to midnight: 12:00 AM - 11:30 PM = 30 minutes
  • From midnight to 7:15 AM: 7 hours 15 minutes
  • Total: 30 minutes + 7 hours 15 minutes = 7 hours 45 minutes

Alternatively, you can think of midnight as 12:00 AM or 0:00, making the calculation easier. The key is to recognize that crossing midnight means you need to add the time before midnight to the time after midnight.

Question: What's the best way to check if my time calculation is correct? Sometimes I'm not sure if my answer makes sense.

Answer: Here are several verification strategies for time calculations:

  • Estimation: Round times to the nearest hour and estimate if your answer is reasonable
  • Reverse calculation: Add your answer back to the start time to see if you get the end time
  • Context check: Does the time make sense in the real-world scenario?
  • Unit check: Ensure your answer is in the correct time units requested

For example, if you calculated that a 2-hour movie lasted 120 minutes, you can quickly verify: 2 × 60 = 120 ✓. This reverse check is especially helpful for conversion problems.