Elapsed Time

Arithmetic
process

Also known as: time passed, duration, time difference

Grade 3-5

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Calculating the amount of time that passes between a start time and an end time, using hours and minutes in base-60 arithmetic rather than base-10. Planning activities, cooking, travel, and scheduling all depend on knowing how much time something takes.

Definition

Calculating the amount of time that passes between a start time and an end time, using hours and minutes in base-60 arithmetic rather than base-10.

💡 Intuition

Imagine a movie starts at 2:15 PM and ends at 4:45 PM. Elapsed time is like counting how many minutes the movie lasted—you hop forward from the start time to the end time.

🎯 Core Idea

Elapsed time measures the duration between two points in time, found by counting forward or subtracting.

Example

\text{Start: } 9{:}20\text{ AM}, \quad \text{End: } 11{:}05\text{ AM} \text{Elapsed time} = 1 \text{ hour } 45 \text{ minutes}

Formula

\text{elapsed time} = \text{end time} - \text{start time}

Notation

Duration is written in hours and minutes (e.g., 2 h 30 min); 1 hour = 60 minutes

🌟 Why It Matters

Planning activities, cooking, travel, and scheduling all depend on knowing how much time something takes.

💭 Hint When Stuck

Count forward from the start time: first jump to the next full hour, then add the remaining minutes to the end time.

Formal View

Elapsed time uses base-60 subtraction: if end = h_2{:}m_2 and start = h_1{:}m_1, then duration = (h_2 - h_1) hours + (m_2 - m_1) minutes, borrowing 1 hour = 60 minutes when m_2 < m_1.

Related Concepts

Telling TimeSubtraction

See Also

skip counting

🚧 Common Stuck Point

Crossing the hour boundary (e.g., from 10:45 to 11:20) requires careful counting since minutes reset at 60, not 100.

⚠️ Common Mistakes

  • Subtracting minutes directly without borrowing when the end minutes are less than start minutes (e.g., 11:05 − 9:20 is not 2:15)
  • Forgetting to account for AM/PM changes when crossing noon or midnight
  • Treating time like base-10 (subtracting 1:45 from 3:20 as 1:75 instead of regrouping)

Frequently Asked Questions

What is Elapsed Time in Math?

Calculating the amount of time that passes between a start time and an end time, using hours and minutes in base-60 arithmetic rather than base-10.

What is the Elapsed Time formula?

\text{elapsed time} = \text{end time} - \text{start time}

When do you use Elapsed Time?

Count forward from the start time: first jump to the next full hour, then add the remaining minutes to the end time.

How Elapsed Time Connects to Other Ideas

To understand elapsed time, you should first be comfortable with telling time and subtraction.

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