Have you ever wondered how long something was? Take a look at this dilemma.

James went to a concert. It was supposed to start at 8 pm, but started late. Instead, it started at 8:08 and ended at 10:12. How long was the concert?

**To figure this out, you will need to know about elapsed time. Pay attention and you will know how to figure this out by the end of the Concept.**

### Guidance

** Elapsed time** tells us how much time passes between two events. We can calculate the elapsed time by figuring out the difference between a start and a stop time.

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, we need to 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. Each time in the problem above represents the number of minutes and hours past noon.

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

Soccer practice lasts for 1 hour 30 minutes.

**Sometimes, we will need to rename the times in a problem in order to subtract them.**

A dance performance starts at 7:30 P.M. and ends at 10:10 P.M. How long does the performance last? Subtract to find the amount of time that passes between those two times.

\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. Rewrite that time as follows. Remember that 1 hour = 60 minutes.

\begin{align*}10:10 & = 10h \ 10 \ min\\ & = 9h + 1h + 10 \ min\\ & = 9h + 60 \ min + 10 \ min\\ & = 9h\ 70 \ min \ \text{or} \ 9:70\end{align*}

Rewrite 10:10 as 9:70. Then subtract.

\begin{align*}& \ \quad 9 : 70\\ &\ \underline{- \ 7 : 30 \;} \\ & \ \quad 2:40\end{align*} The dance performance lasts for 2 hours 40 minutes.

**What about when an event starts in the morning and ends in the afternoon, how do we calculate elapsed time then?**

To do this, we are going to need a different strategy.

Try a few of these on your own.

#### Example A

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

**Solution: 2 hours and 5 minutes**

#### Example B

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

**Solution: 2 hours and 50 minutes**

#### Example C

Jake walked from 7:15 am until 9:00 am, how long was his walk?

**Solution: 1 hour and 45 minutes**

Here is the original problem once again.

James went to a concert. It was supposed to start at 8 pm, but started late. Instead, it started at 8:08 and ended at 10:12. How long was the concert?

To figure this out, we can simply subtract the times. Let's start with the later time first.

\begin{align*}10:12 - 8:08\end{align*}

Next, we simply subtract.

\begin{align*}10:12 - 8:08 = 2:04\end{align*}

**This is our answer.**

### Vocabulary

- Hour
- A measurement of time that is 60 minutes long

- Minute
- A measurement of time that is 60 seconds long

- Second
- A measurement of time that is the smallest unit of time

### Guided Practice

The soccer game started at 10:00 am and ended at 1:40 pm. How long was the game? To figure this out, we must first count up to noon. From 10 to Noon is 2 hours, so we need to keep track of that time. The elapsed time is 2 hours. Then we can figure out how long it was from noon to 1:40 pm. That is 1 hour and 40 minutes. Finally, we can add the two figures together.

\begin{align*}& \quad \ 2 : 00\\ & \underline{+ \ \ 1 : 40}\\ & \quad \ 3 : 40 \ minutes\end{align*}

### Video Review

James Sousa Operations with Time

### Practice

Directions: Calculate the elapsed time in each problem.

1. If a movie starts at 7:15 and ends at 9:20, how long was the movie?

2. If a movie starts at 7:15 and ends at 9:20, but has ten minutes of previews, how long is the movie?

3. If a movie was 1:50 minutes and started at 8 pm, what time would the movie end?

4. If there were an additional 15 minutes of previews in this movie, what time would the movie end?

5. If there was also a 10 minute intermission, what time would the movie end?

6. A hike lasted for 2 hours. If it started at 8:20, what time did it end?

7. A hike lasted for 3 hours and five minutes. If it started at 9:05, what time did it end?

8. A walk started at 7:09 and went until 10:45. How long was the walk?

9. If a movie starts at 5:15 and ends at 6:20, how long was the movie?

10. Jesse rode his bike from 8 pm until 9:07, how long did he ride?

11. Jesse went swimming from 9:07 until 10:03, how long did he swim?

12. If Marcy went swimming twice as long as Jesse, how long did she swim?

13. Caleb went swimming half as long as Jesse, how long did he swim?

14. Samuel attended an assembly that lasted for four hours. If it started at 8:32, what time did it end?

15. If the Campbell family went to the beach for five hours and 11 minutes and they left at 7 pm, what time did they arrive?