Elapsed time: The amount of time that passes between a start time and an end time. Formula: Elapsed Time = End Time - Start Time
- Identify the start time (2:15 PM)
- Identify the end time (3:40 PM)
- Calculate the difference using time subtraction
End time: 3:40 PM
Start time: 2:15 PM
We need to subtract: 3:40 - 2:15
Minutes: 40 - 15 = 25 minutes
Hours: 3 - 2 = 1 hour
Total elapsed time = 1 hour 25 minutes
Sarah spent 1 hour 25 minutes reading.
• Elapsed Time Formula: End Time - Start Time = Elapsed Time
• Time Conversion: 1 hour = 60 minutes
• Subtraction: Subtract hours and minutes separately
Crossing over noon/midnight: When calculating elapsed time across AM/PM changes, convert to 24-hour format or count in segments.
From 11:30 AM to 12:00 PM = 30 minutes
From 12:00 PM to 1:00 PM = 1 hour
From 1:00 PM to 1:15 PM = 15 minutes
Total = 30 minutes + 1 hour + 15 minutes = 1 hour 45 minutes
11:30 AM = 11:30
1:15 PM = 13:15
Since 15 < 30, we borrow: 13:15 becomes 12:75
12:75 - 11:30 = 1 hour 45 minutes
The movie lasted 1 hour 45 minutes.
• AM/PM Transition: Count in segments when crossing noon or midnight
• Time Conversion: 60 minutes = 1 hour
• Addition: Sum all time segments for total elapsed time
Finding end time: When start time and duration are known, add the duration to the start time. Formula: End Time = Start Time + Duration
Start time: 8:45 AM
Add 2 hours: 8:45 AM + 2 hours = 10:45 AM
Current time: 10:45 AM
Add 30 minutes: 10:45 AM + 30 minutes = 11:15 AM
Minutes added: 45 + 30 = 75 minutes (≥ 60, so convert)
75 minutes = 1 hour 15 minutes
So final time is 11:15 AM
The bus arrived at 11:15 AM.
• End Time Formula: Start Time + Duration = End Time
• Addition sequence: Add hours first, then minutes
• Overflow check: If minutes ≥ 60, convert to hours
Elapsed time: The duration between two events; the amount of time that passes between a start time and an end time.
Start time: The exact moment an event begins.
End time: The exact moment an event concludes.
Duration: The length of time an event lasts; synonymous with elapsed time.
Time interval: The difference between two specific times.
- Direct subtraction: End time - Start time
- Segment method: Break into hours and minutes
- Number line method: Visual representation of time
- 24-hour conversion: Convert to military time
- Borrowing method: When minutes need adjustment
• 1 minute = 60 seconds
• 1 hour = 60 minutes = 3,600 seconds
• 1 day = 24 hours = 1,440 minutes
• 1 week = 7 days
• 1 year = 365 days (366 in leap years)
Borrowing in time subtraction: When minutes in end time are less than minutes in start time, borrow 1 hour (60 minutes) from the hour part.
End time: 3:30 PM
Start time: 1:55 PM
We need to subtract: 3:30 - 1:55
Minutes in end time (30) < Minutes in start time (55)
We need to borrow: 3:30 = 2:90 (borrow 1 hour = 60 minutes)
New end time: 2:90 PM
Start time: 1:55 PM
Hours: 2 - 1 = 1 hour
Minutes: 90 - 55 = 35 minutes
Total elapsed time = 1 hour 35 minutes
The basketball game lasted 1 hour 35 minutes.
• Borrowing Rule: When minutes in minuend < subtrahend, borrow 1 hour = 60 minutes
• Subtraction: Subtract hours and minutes separately
• Verification: Add elapsed time to start time to verify end time
Multi-day elapsed time: When calculating elapsed time across multiple days, calculate full days plus partial days.
Thursday to Friday = 1 full day
Friday to Saturday = 1 full day
Total full days = 2 days
On Saturday: From 9:20 AM to 2:45 PM
9:20 AM to 12:00 PM = 2 hours 40 minutes
12:00 PM to 2:00 PM = 2 hours
2:00 PM to 2:45 PM = 45 minutes
Total = 2 hours 40 minutes + 2 hours + 45 minutes = 5 hours 25 minutes
Full days: 2 days
Partial day: 5 hours 25 minutes
Total elapsed time = 2 days 5 hours 25 minutes
2 full days = 2 × 24 hours = 48 hours
5 hours 25 minutes = 5.42 hours
Total = 48 + 5.42 = 53.42 hours = 53 hours 25 minutes
The camping trip lasted 2 days 5 hours 25 minutes.
• Multi-day calculation: Count full days separately from partial days
• Time within a day: Use regular elapsed time calculation for partial days
• Unit conversion: 1 day = 24 hours for verification purposes
Elapsed time: The duration between two events; the amount of time that passes between a start time and an end time.
Start time: The exact moment an event begins.
End time: The exact moment an event concludes.
Duration: The length of time an event lasts; synonymous with elapsed time.
Time interval: The difference between two specific times.
- Direct subtraction: End time - Start time (most common method)
- Segment method: Break complex time spans into manageable parts
- Number line method: Visual representation of time progression
- 24-hour conversion: Convert to military time for complex calculations
- Borrowing method: When minutes need adjustment during subtraction
• 1 minute = 60 seconds
• 1 hour = 60 minutes = 3,600 seconds
• 1 day = 24 hours = 1,440 minutes
• 1 week = 7 days
• 1 year = 365 days (366 in leap years)
Type 1 - Find Elapsed Time: Given start and end time, calculate duration.
Type 2 - Find End Time: Given start time and duration, calculate end time.
Type 3 - Find Start Time: Given end time and duration, calculate start time.
Type 4 - Multi-day calculations: Problems spanning multiple days.
Type 5 - Time zone problems: Calculations across different time zones.
Segment Method: Break complex time spans into manageable parts (e.g., from start time to next hour, then full hours, then remaining minutes).
24-Hour Conversion: Convert AM/PM times to 24-hour format to avoid confusion.
Visualization: Draw number lines or clocks to visualize the time span.
Verification: Always check by working backwards from your answer.
• Formula Triangle: E = E - S (Elapsed = End - Start)
• Time Rhyme: "Sixty minutes make an hour, sixty seconds make a minute power!"
• Borrowing Reminder: "When minutes go negative, borrow 60 from the hour next!"
Questions & Answers
Question: I get confused when subtracting time like 3:30 - 1:55 because 30 is smaller than 55. How do I handle this?
Answer: This is called "borrowing" in time calculations:
- When minutes in the top time are smaller than minutes in the bottom time, you need to borrow
- Borrow 1 hour from the hour part, which equals 60 minutes
- Add these 60 minutes to the minutes part
- Reduce the hour part by 1
For your example: 3:30 - 1:55
Since 30 < 55, we borrow: 3:30 becomes 2:90 (3 hours - 1 hour = 2 hours, 30 minutes + 60 minutes = 90 minutes)
Now subtract: 2:90 - 1:55 = 1 hour 35 minutes
This is just like regular subtraction, but with time units!
Question: How do I calculate elapsed time that crosses from AM to PM, like from 11:30 AM to 1:15 PM?
Answer: There are two approaches to solve this type of problem:
Method 1: Break into segments
- From 11:30 AM to 12:00 PM = 30 minutes
- From 12:00 PM to 1:00 PM = 1 hour
- From 1:00 PM to 1:15 PM = 15 minutes
- Total = 30 minutes + 1 hour + 15 minutes = 1 hour 45 minutes
Method 2: Convert to 24-hour format
- 11:30 AM = 11:30
- 1:15 PM = 13:15
- Subtract normally: 13:15 - 11:30
- Since 15 < 30, borrow: 13:15 becomes 12:75
- 12:75 - 11:30 = 1 hour 45 minutes
Both methods give the same result!
Question: What's the easiest way to remember the time conversions like hours to minutes?
Answer: Here are some helpful memory aids for time conversions:
- Think of a clock: A clock has 60 minutes for each hour hand movement
- Rhyme: "Sixty minutes make an hour, sixty seconds make a minute power!"
- Use your hands: Count 60 seconds while holding up fingers for each 10 seconds
- Practice conversions daily: How many minutes until lunch? How many seconds in 2 minutes?
Here's the complete set to memorize:
- 1 minute = 60 seconds
- 1 hour = 60 minutes
- 1 day = 24 hours
- 1 week = 7 days
Remember: each unit is larger than the previous one, so multiply to go bigger, divide to go smaller!