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 given information: Start time (3:15 PM) and duration (1 hour 30 minutes)
- Determine what is being asked: End time
- Use the formula: End Time = Start Time + Duration
- Calculate the answer
Start time: 3:15 PM
Duration: 1 hour 30 minutes
Need to find: End time
Start time: 3:15 PM
Add 1 hour: 3:15 PM + 1 hour = 4:15 PM
Current time: 4:15 PM
Add 30 minutes: 4:15 PM + 30 minutes = 4:45 PM
End time: 4:45 PM
Start time: 3:15 PM
Elapsed time: 4:45 PM - 3:15 PM = 1 hour 30 minutes ✓
Maria finished practicing piano at 4:45 PM.
• End Time Formula: Start Time + Duration = End Time
• Time Conversion: 1 hour = 60 minutes
• Addition: Add hours first, then minutes
Crossing over noon/midnight: When calculating elapsed time across AM/PM changes, convert to 24-hour format or count in segments.
Start time: 11:30 AM
End time: 1:45 PM
Need to find: Elapsed time
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 1:45 PM = 45 minutes
Total = 30 minutes + 1 hour + 45 minutes = 2 hours 15 minutes
11:30 AM = 11:30
1:45 PM = 13:45
13:45 - 11:30 = 2 hours 15 minutes
The movie lasted 2 hours and 15 minutes.
• Elapsed Time Formula: End Time - Start Time = Elapsed Time
• Time Conversion: 60 minutes = 1 hour
• Addition: Sum all time segments for total elapsed time
Finding start time: When end time and duration are known, subtract the duration from the end time. Formula: Start Time = End Time - Duration
End time: 4:20 PM
Duration: 2 hours 50 minutes
Need to find: Start time
Start time = End time - Duration
Start time = 4:20 PM - 2 hours 50 minutes
Minutes in end time (20) < Minutes in duration (50)
We need to borrow: 4:20 = 3:80 (borrow 1 hour = 60 minutes)
New end time: 3:80 PM
Duration: 2 hours 50 minutes
Hours: 3 - 2 = 1 hour
Minutes: 80 - 50 = 30 minutes
The train left at 1:30 PM.
• Start Time Formula: End Time - Duration = Start Time
• Borrowing Rule: When minutes in minuend < subtrahend, borrow 1 hour = 60 minutes
• Subtraction: Subtract hours and minutes separately
Start time: The time when an activity begins
End time: The time when an activity finishes
Duration: The total amount of time an activity takes
Elapsed time: The amount of time that passes between two events
AM: Ante meridiem (before noon)
PM: Post meridiem (after noon)
- Read the problem carefully: Identify what information is given and what is being asked
- Highlight important information: Note start times, end times, durations, etc.
- Decide which formula to use: Determine if you need to find elapsed time, start time, or end time
- Set up the equation: Write the appropriate formula with the known values
- Solve the equation: Calculate the answer using proper time arithmetic
- Check your answer: Verify it makes sense in the context of the problem
• 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.
Start time: 2:45 PM
End time: 4:20 PM
Need to find: Elapsed time
Elapsed time = End time - Start time
Elapsed time = 4:20 PM - 2:45 PM
Minutes in end time (20) < Minutes in start time (45)
We need to borrow: 4:20 = 3:80 (borrow 1 hour = 60 minutes)
New end time: 3:80 PM
Start time: 2:45 PM
Hours: 3 - 2 = 1 hour
Minutes: 80 - 45 = 35 minutes
The soccer game lasted 1 hour and 35 minutes.
• Elapsed Time Formula: End Time - Start Time = Elapsed Time
• Borrowing Rule: When minutes in minuend < subtrahend, borrow 1 hour = 60 minutes
• Subtraction: Subtract hours and minutes separately
Multi-day elapsed time: When calculating elapsed time across multiple days, calculate full days plus partial days.
Tuesday to Wednesday = 1 full day
Wednesday to Thursday = 1 full day
Total full days = 2 days
On Thursday: From 9:15 AM to 3:30 PM
9:15 AM to 12:00 PM = 2 hours 45 minutes
12:00 PM to 3:00 PM = 3 hours
3:00 PM to 3:30 PM = 30 minutes
Total = 2 hours 45 minutes + 3 hours + 30 minutes = 6 hours 15 minutes
Full days: 2 days
Partial day: 6 hours 15 minutes
Total elapsed time = 2 days 6 hours 15 minutes
Alternative: Convert to minutes
2 full days = 2 × 24 × 60 = 2,880 minutes
6 hours 15 minutes = (6 × 60) + 15 = 375 minutes
Total = 2,880 + 375 = 3,255 minutes
The field trip lasted 2 days, 6 hours, and 15 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.
Word problem: A mathematical problem presented in a real-life context using narrative text.
- Read carefully: Understand what the problem is asking
- Identify information: Note all given times and durations
- Determine question: Identify what needs to be found
- Select formula: Choose the correct formula based on the question
- Solve: Calculate the answer using proper procedures
- Check: Verify the answer makes sense in context
• 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)
For finding elapsed time: "how long", "duration", "time passed", "length of time", "how much time"
For finding end time: "what time", "when did", "finished at", "ended at", "arrived at"
For finding start time: "started at", "began at", "left at", "departed at", "when did it begin"
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 4:20 - 2:45 because 20 is smaller than 45. 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: 4:20 - 2:45
Since 20 < 45, we borrow: 4:20 becomes 3:80 (4 hours - 1 hour = 3 hours, 20 minutes + 60 minutes = 80 minutes)
Now subtract: 3:80 - 2:45 = 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 1:45 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 1:45 PM = 45 minutes
- Total = 30 minutes + 1 hour + 45 minutes = 2 hours 15 minutes
Method 2: Convert to 24-hour format
- 11:30 AM = 11:30
- 1:45 PM = 13:45
- Subtract normally: 13:45 - 11:30 = 2 hours 15 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!