James is reading a book. He started at 4:00 p.m. and before he knew it, it was 8:30 p.m. How much time did James spend reading?

In this concept, you will learn how to find elapsed time.

### Calculating Elapsed Time

**Elapsed time** is the amount of time that has passed between two events. You can calculate the elapsed time by figuring out the difference between the start and stop time.

Here is an elapsed time problem.

Soccer practice begins at 3:15 p.m. and ends at 4:45 p.m. Determine how long soccer practice lasts.

To solve this problem, set up a subtraction problem that could be used to find the number of hours and minutes that pass between those two times.

Subtract the starting time from the stopping time. Remember that both times represent the number of hours and minutes past noon.

\begin{align*}4 : 45\\ \underline{- \ 3 : 15}\\ 1 : 30\end{align*}

Soccer practice lasts for 1 hour 30 minutes.

Here is another problem.

A dance performance starts at 7:30 p.m. and ends at 10:10 p.m. How long does the performance last?

Subtract the starting time from the stopping time.

\begin{align*}& \quad 10 : 10\\ &\ \underline{- \; 7 : 30\;}\end{align*}

You cannot subtract 30 minutes from 10 minutes, so you must rewrite 10:10. Remember, 10:10 stands for 10 hours 10 minutes. Borrow from the hour unit. 1 hour equals 60 minutes. Add 60 minutes to the 10 minutes.

\begin{align*} \cancel{10}^9 &: \cancel{10}^{70}\\ - \ 7 \ \ \ &: \ 30 \\ \hline 2 \ \ \ &: \ 40\end{align*}

Events can also occur before noon (a.m.) and end after noon (p.m.). When that happens, finding the elapsed time requires an additional step. This is a result of using a 12-hour clock.

Here is an example.

John goes to school at 8:00 a.m. and returns home at 3:00 p.m. How long was John at school?

You might think that the elapsed time is 5 hours, which would be incorrect. Before finding the difference, add 12 hours to 3:00 p.m.

\begin{align*} 12 : 00\\ \ + \ \ 1 : 40\\ \hline 13 : 40 \end{align*}

Remember that the day starts at midnight. 8:00 a.m. is 8 hours into the day and 3:00 p.m. is actually 15 hours into the day. Rewrite 3:00 p.m. as 15:00 and find the elapsed time.

\begin{align*}15 : 00\\ \ - \ \ 8 : 00 \\ \hline 7 : 00\end{align*}

John was at school for 7 hours.

### Examples

#### Example 1

Earlier, you were given a problem about James reading his book.

James started at 4:00 p.m. and stopped at 8:30 p.m. Find the elapsed time between the start and end time.

Subtract the start time from the end time.

James spent 4 hours 30 minutes reading.

#### Example 2

Find the elapsed time.

The soccer game started at 10:00 a.m. and ended at 1:40 p.m. How long was the game?

The start and stop time occur during different parts of the day, a.m. and p.m.

First, rewrite 1:40 pm. Add 12 hours to the p.m. time.

\begin{align*}& \quad \ 12 : 00\\ & \underline {+ \ \ 1 \ \ \ : 40}\\ & \quad \ 13 : 40 \ \end{align*}

Then, subtract the start time from the end time.

\begin{align*}& \quad \ 13 : 40\\ & \underline{- \ \ 10 \ : 00}\\ & \quad \ 3\ \ : 40 \ \end{align*}

#### Example 3

The game started at 9:10 am and ended at 11:15 am. What was the length of the game?

Subtract the start time from the end time.

\begin{align*}& \quad \ 11: 15\\ & - \ \ 9\ \ \ : 10\\ \hline & \quad \ 2\ \ : 05\ \end{align*}

The elapsed time is 2 hours and 5 minutes.

#### Example 4

The movie started at 7:30 pm and ended at 10:20 pm. How long was the movie?

Subtract the start time from the end time. Borrow 60 minutes from the hour place value.

\begin{align*} \cancel{10}^9 &: \cancel{20}^{80}\\
- \ 7 \ \ \ &: \ 30 \\
\hline
2 \ \ \ &: \ 50\end{align*}

The elapsed time is 2 hours and 50 minutes.

#### Example 5

Jake walked from 7:15 am until 9:00 am. How long was his walk?

Subtract the start time from the end time. Borrow 60 minutes from the hour place value.

\begin{align*} \cancel{9}^8&: \cancel{00}^{60}\\ - \ 7 \ \ \ &: \ 15\\ \hline 1\ \ \ &: \ 45\end{align*}

The elapsed time is 1 hour and 45 minutes.

### Review

Calculate the elapsed time in each problem.

- If a movie starts at 7:15 p.m. and ends at 9:20 p.m., how long was the movie?
- If a movie starts at 7:15 p.m. and ends at 9:20 p.m., but has ten minutes of previews, how long is the movie?
- If a movie was 1 hour and 50 minutes and started at 8:00 p.m., what time would the movie end?
- If there were an additional 15 minutes of previews in this movie, what time would the movie end?
- If there was also a 10 minute intermission, what time would the movie end?
- A hike lasted for 2 hours. If it started at 8:20 a.m., what time did it end?
- A hike lasted for 3 hours and 5 minutes. If it started at 9:05 a.m., what time did it end?
- A walk started at 7:09 a.m. and went until 10:45 a.m. How long was the walk?
- If a movie starts at 5:15 p.m. and ends at 6:20 p.m., how long was the movie?
- Jesse rode his bike from 8:00 p.m. until 9:07 p.m., how long did he ride?
- Jesse went swimming from 9:07 a.m. until 10:03 a.m., how long did he swim?
- If Marcy went swimming twice as long as Jesse, how long did she swim?
- Caleb went swimming half as long as Jesse, how long did he swim?
- Samuel attended an assembly that lasted for four hours. If it started at 8:32 a.m., what time did it end?
- If the Campbell family went to the beach for 5 hours and 11 minutes and they left the beach at 7:00 p.m., what time did they arrive?

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.15.