6.6: Elapsed Time
Introduction
Beating the Clock
While working, Travis accidentally loses his measuring tape. He searches everywhere, but can’t seem to find it.
“Uncle Larry, I can’t find my measuring tape,” Travis says. “I’m going to ride my bike to the hardware store and get a new one.”
“Alright Travis, but we are having a meeting at 11 and I would like you to be back for it,” Uncle Larry says.
Travis looks down at his watch. It is 10:15. He knows that he can make it, but he will need to hurry.
Travis dashes out the door and jumps onto his bike. He rides to the store, gets his measuring tape and returns back.
It takes Travis \begin{align*}\frac{1}{2}\end{align*} hour to ride to the store and back. He gets a little distracted in the store, but after 10 minutes, he finds and buys the measuring tape.
Did Travis make it back in time for the meeting? You will need to learn some information about calculating time to be sure.
Pay close attention and you will be able to figure this problem out at the end of the lesson.
What You Will Learn
In the following lesson, you will learn the following skills:
- Add and subtract measures of time.
- Find elapsed time between given start and stop times.
- Solve real-world problems involving elapsed time.
Teaching Time
I. Add and Subtract Measures of Time
We add and subtract units of time every day. Sometimes, we are trying to figure out whether we will be on time or late. In other situations, we are trying to figure out a movie time or the time to meet a friend, or how long the soccer game actually lasted. To calculate units of time, we are going to need to know how to convert minutes to seconds to hours.
One of the first things that you need to know how to do when working with time is to convert different units.
How do we convert units?
The easiest way is to simply multiply or divide. Sometimes, you will be able to accomplish this using mental math. In fact, you should try to figure things out in your head whenever possible. In this lesson, you can see the work the long way too, but mental math is almost always quicker.
Example
120 minutes = _______ hours
First, try to figure this one out in your head using mental math. Now let’s look at the solution.
To convert a smaller unit to a larger unit, we divide.
There are 60 minutes in one hour, so we divide 120 minutes by 60 and we get 2.
120 minutes = 2 hours
We can also do this the other way around.
Example
How many minutes are there in 4 hours?
To solve this problem, we are going to from a larger unit to a smaller unit, so we multiply.
4 \begin{align*}\times\end{align*} 60 \begin{align*}=\end{align*} 240
There are 240 minutes in 4 hours.
Try a few of these on your own.
- 180 minutes = ______ hours
- 5 hours = ______ minutes
- 180 seconds = ______ minutes
Check your answers with a friend.
What about when you have fractional units of time?
Sometimes, we measure time using fractional units. For example, we might use the phrase \begin{align*}`` \frac{3}{4}\end{align*} of an hour or \begin{align*}\frac{1}{2}\end{align*} an hour.” We can also figure out how many minutes these fractional units of time are.
Here are some given fractional units of time. We can figure out whether or not these measures are accurate.
Let’s test out and prove that \begin{align*}\frac{1}{4}\end{align*} hour is equal to 15 minutes. If we know that there are 60 minutes in one hour then we can multiply \begin{align*}\frac{1}{4}(60)\end{align*} and that will give us the number of minutes.
\begin{align*}\frac{1}{4} (60) = \frac{60}{4} = 15\end{align*}
Our work is accurate.
We can also figure out any fraction of an hour using this method.
Example
What is \begin{align*}\frac{1}{8}\end{align*} of an hour in minutes?
To figure this out, we multiply \begin{align*}\frac{1}{8}\end{align*} times 60 since we want our answer in minutes.
\begin{align*}\frac{1}{8}(60) = \frac{60}{8} = 7.5\end{align*}
Our answer is 7.5 minutes or \begin{align*}7 \frac{1}{2}\end{align*} minutes.
Try a few of these conversions on your own.
- How many minutes is \begin{align*}\frac{1}{5}\end{align*} of an hour?
- How many minutes is \begin{align*}\frac{1}{6}\end{align*} of an hour?
Take a few minutes to check your work with a partner.
II. Find Elapsed Time Between Given Start and Stop Times
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.
Example
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.
Example
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 past noon.
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. Let’s look at an example.
Example
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.
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*}
Try a few of these on your own.
- The game started at 9:10 am and ended at 11:15 am. What was the length of the game?
- The movie started at 7:30 pm and ended at 10:20 pm. How long was the movie?
Check your work with a peer.
Real Life Example Completed
Beating the Clock
You have learned all about how to calculate units of time and elapsed time. Now let’s go back to our original problem.
While working, Travis accidentally loses his measuring tape. He searches everywhere, but can’t seem to find it.
“Uncle Larry, I can’t find my measuring tape,” Travis says. “I’m going to ride my bike to the hardware store and get a new one.”
“Alright Travis, but we are having a meeting at 11 and I would like you to be back for it,” Uncle Larry says.
Travis looks down at his watch. It is 10:15. He knows that he can make it, but he will need to hurry.
Travis dashes out the door and jumps onto his bike. He rides to the store, gets his measuring tape and returns back.
It takes Travis \begin{align*}\frac{1}{2}\end{align*} hour to ride to the store and back. He gets a little distracted in the store, but after 10 minutes, he finds and buys the measuring tape.
Did Travis make it back in time for the meeting? You will need to learn some information about calculating time to be sure.
First, let’s go back and underline all of the important information.
Now we need to add up the time that it took Travis to go to the store, buy the measuring tape and get back.
Riding time = 30 minutes of riding time total-15 minutes there and 15 minutes back.
10 minutes in the store.
30 + 10 = 40 total minutes
How much time was there from 10:15 when Travis left until the meeting at 11:00?
11 - 10:15 = 45 minutes
45 - 40 = 5 minutes
Travis arrived back at the work site with five minutes to spare.
Vocabulary
Here are the vocabulary words that can be found in this lesson.
- Elapsed Time
- the time from the start of an event to the end of the event.
- Units of Time
- how we measure time using seconds, minutes and hours.
Technology Integration
James Sousa Operations with Time
Other Sites:
- http://www.mrnussbaum.com/elapse5.htm – This is not a video, but it is an interactive site that helps students to calculate elapsed time.
Time to Practice
Directions: Add the following units of time.
1. 15 minutes plus 60 minutes = ______
2. 10 minutes and twenty minutes = ______
3. 15 seconds and 45 seconds = ______
4. 50 minutes and 20 minutes = ______ hours ______ minutes
5. 75 minutes and 15 minutes = ______ hours
6. 35 minutes and 10 minutes = ______ minutes
7. 60 minutes and 10 minutes = ______ hours ______ minutes
8. 75 minutes and 20 minutes = ______ hours ______ minutes
9. 120 minutes and ten minutes = ______ hours ______ minutes
10. 300 seconds and 5 minutes = ______ minutes
Directions: Convert the following units and fractional units of time.
11. 3000 seconds = ______ minutes
12. 4 hours = ______ minutes
13. 6000 seconds = ______ hours ______ minutes
14. 120 minutes = ______ hours
15. 360 minutes = ______ hours
16. 300 minutes = ______ hours
17. 12,000 seconds = ______ minutes
18. \begin{align*}\frac{1}{4}\end{align*} hour = ______ minutes
19. \begin{align*}\frac{1}{8}\end{align*} hour = ______ minutes
20. \begin{align*}\frac{1}{2}\end{align*} hour = ______ minutes
Directions: Calculate the elapsed time in each problem.
21. If a movie starts at 7:15 and ends at 9:20, how long was the movie?
22. If a movie starts at 7:15 and ends at 9:20, but has ten minutes of previews, how long is the movie?
23. If a movie was 1:50 minutes and started at 8 pm, what time would the movie end?
24. If there were an additional 15 minutes of previews in this movie, what time would the movie end?
25. If there was also a 10 minute intermission, what time would the movie end?