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Calculating Elapsed Time

This lesson explains how to calculate elapsed time, the amount of time that passes between a start time and an end time. Students learn the counting-up method on a number line and the subtraction method, including problems that cross the hour mark or move between AM and PM.

What Is Elapsed Time?

Elapsed time is simply the amount of time that passes between a starting time and an ending time. If a movie starts at 4:15 p.m. and ends at 6:30 p.m., the elapsed time is how long the movie lasted. Calculating elapsed time is a skill you use constantly, whether you're timing a trip, figuring out how long a class lasts, or planning a schedule. Before working with elapsed time, it helps to be comfortable reading and writing time on both analog and digital clocks.

The Counting-Up Method

The most reliable way to calculate elapsed time is to count up from the start time to the end time in friendly chunks, usually jumping to the next multiple of ten minutes, then to the next whole hour, and finally to the exact end time. Each jump is added together at the end to get the total elapsed time.

Suppose a bus leaves the station at 9:15 and arrives at 1:00. Instead of trying to subtract these times directly, count up in stages:

From 9:15 to 10:00 is 45 minutes.
From 10:00 to 1:00 is 3 hours.

Adding the jumps together, \( 45 \) minutes \( + 3 \) hours \( = 3 \) hours \( 45 \) minutes. That is the total elapsed time for the trip.

Calculating Elapsed Time by Subtraction

When the start and end time are within the same block of hours and minutes, you can subtract directly. Subtract the hours from the hours and the minutes from the minutes.

Example: A study session starts at 2:20 and ends at 5:50.

Hours: \( 5 - 2 = 3 \). Minutes: \( 50 - 20 = 30 \). The elapsed time is 3 hours 30 minutes.

This subtraction method gets trickier when the minutes in the end time are smaller than the minutes in the start time, because you cannot subtract a bigger number of minutes from a smaller one. In that case, regroup by borrowing 1 hour and converting it into 60 minutes before subtracting, just like regrouping in ordinary subtraction with numbers.

Example: A hike starts at 8:40 and ends at 11:10.

Since \( 10 \) minutes is less than \( 40 \) minutes, borrow 1 hour from the 11 (making it 10 hours) and add 60 minutes to the 10, making it 70 minutes. Now subtract: hours \( 10 - 8 = 2 \), minutes \( 70 - 40 = 30 \). The hike lasted 2 hours 30 minutes.

Working Across AM and PM

Some elapsed time problems cross from morning into afternoon, or from one day into the next. Before subtracting or counting up, make sure both times are written clearly with AM or PM so you don't lose track of whether 12 hours have passed. Reviewing understanding AM and PM can help you avoid mixing up midnight and noon in these problems.

Example: A flight departs at 10:45 a.m. and lands at 1:15 p.m. Counting up: from 10:45 a.m. to 11:00 a.m. is 15 minutes, from 11:00 a.m. to 1:00 p.m. is 2 hours, and from 1:00 p.m. to 1:15 p.m. is 15 minutes. Adding these, \( 15 + 120 + 15 = 150 \) minutes, which equals 2 hours 30 minutes.

Checking Your Work

A quick way to check any elapsed time answer is to count backward from the end time by the amount you calculated. If counting back lands exactly on the start time, your answer is correct. This habit is especially useful on elapsed time word problems, where a small misread of AM or PM can throw off the whole answer.

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