Calculating Elapsed Time and Intervals in Minutes - Third Grade Mathematics

Elapsed time is the amount of time that passes from the start of an activity to the end of that activity. Whether you are finding out how long a movie lasts, how much time you have for soccer practice, or what time dinner will be ready, calculating elapsed time is an indispensable life skill. In this chapter, you will master finding start times, end times, and elapsed intervals using open number lines and the zoom-in mountain-hill-rock strategy.

What Is Elapsed Time?

Elapsed time measures the duration between two events.

[ Start Time ] ------ Elapsed Time (Duration) ------> [ End Time ]

Every elapsed time situation connects three components:
1. Start Time: When the event begins.

2. Elapsed Time: How long the event lasts (hours and minutes).

3. End Time: When the event finishes.


If you know any two of these components, you can find the third!

The Open Number Line Strategy

An open number line is the most reliable visual tool for calculating elapsed time. You do not need tick marks for every minute; you simply hop forward or backward using convenient chunks of time.

The Three Types of Hops:

  • Mountains = 1 Hour hops (60 minutes)
  • Hills = 5, 10, 15, or 30 Minute hops
  • Rocks = 1 Minute hops
   /\ (Mountain = 1 hour)
  /   /____\       ( ) (Hill = 10 or 5 min)     . (Rock = 1 min)

Case 1: Finding Elapsed Time Given Start and End Times

Problem: A basketball game started at 3:15 p.m. and ended at 4:42 p.m. How long did the game last?

Step 1: Place 3:15 p.m. at the start of your number line. Step 2: Take a 1-hour mountain jump: 3:15 p.m. + 1 hour = 4:15 p.m. (Total elapsed: 1 hour) Step 3: Can you take another 1-hour jump? No, because 4:15 + 1 hour = 5:15, which is past the end time of 4:42 p.m. Step 4: Take friendly minute jumps from 4:15 to 4:42:
- Hop 15 minutes to reach 4:30 p.m.

- Hop 10 minutes to reach 4:40 p.m.

- Hop 2 minutes to reach 4:42 p.m.
Step 5: Add all your jumps together: 1 hour + 15 min + 10 min + 2 min = 1 hour and 27 minutes!

3:15        +1 hour -> 4:15    +15 min -> 4:30   +10 min -> 4:40  +2 min -> 4:42
+------------------------+------------------+---------------+--------------+
<------- 1 hr ----------><---- 15 min -----><--- 10 min ---><--- 2 min --->
Total Elapsed Time = 1 hour 27 minutes

Case 2: Finding End Time Given Start Time and Elapsed Time

Problem: Maya started baking bread at 10:35 a.m. The bread needs to bake for 45 minutes. What time will the bread be done?

Strategy: Make friendly jumps to the next full hour!
- Start at 10:35 a.m.

- How many minutes until 11:00 a.m.? Exactly 25 minutes! (60 - 35 = 25).

- Hop 25 minutes to land at 11:00 a.m.

- How much baking time is left from the 45 minutes?
45 - 25 = 20 minutes left!
- Hop the remaining 20 minutes past 11:00 a.m. to land at 11:20 a.m.
The bread will be done at 11:20 a.m.

Case 3: Finding Start Time Given End Time and Elapsed Time

Problem: A train arrived at the station at 2:10 p.m. The trip took 50 minutes. What time did the train depart?

Strategy: Hop backward on the number line!
- Start at the end: 2:10 p.m.

- Hop backward 10 minutes to reach the friendly hour of 2:00 p.m. (40 minutes remain).

- Hop backward the remaining 40 minutes into the previous hour:
60 - 40 = 20 minutes. Landing spot: 1:20 p.m. The train departed at 1:20 p.m.

Chapter Practice Exercises

  1. Find the elapsed time for each activity: a. Start: 1:15 p.m. | End: 2:45 p.m. b. Start: 8:20 a.m. | End: 9:05 a.m. c. Start: 4:35 p.m. | End: 6:10 p.m. d. Start: 11:50 a.m. | End: 1:12 p.m.
  2. Find the end time: a. Start: 3:25 p.m. | Elapsed: 35 minutes b. Start: 7:40 a.m. | Elapsed: 1 hour 25 minutes c. Start: 1:18 p.m. | Elapsed: 47 minutes
  3. Find the start time: a. End: 5:00 p.m. | Elapsed: 45 minutes b. End: 8:15 p.m. | Elapsed: 1 hour 30 minutes
  4. A science experiment began at 9:48 a.m. and finished at 10:32 a.m. How many minutes did the experiment take?
  5. Oliver has soccer practice from 4:15 p.m. to 5:30 p.m. His friend Leo has band practice from 4:30 p.m. to 5:40 p.m. Whose practice is longer, and by how many minutes?

Solutions and Step-by-Step Answers

  1. Elapsed times: a. 1:15 to 2:15 = 1 hour; 2:15 to 2:45 = 30 minutes. Elapsed: 1 hour 30 minutes. b. 8:20 to 9:00 = 40 minutes; 9:00 to 9:05 = 5 minutes. Elapsed: 45 minutes. c. 4:35 to 5:35 = 1 hour; 5:35 to 6:00 = 25 minutes; 6:00 to 6:10 = 10 minutes. Elapsed: 1 hour 35 minutes. d. 11:50 to 12:50 = 1 hour; 12:50 to 1:00 = 10 minutes; 1:00 to 1:12 = 12 minutes. Elapsed: 1 hour 22 minutes.
  2. End times: a. 3:25 + 35 min: 3:25 + 35 min = 3:60 = 4:00 p.m. b. 7:40 + 1 hr 25 min: 7:40 + 1 hr = 8:40; 8:40 + 20 min = 9:00; 9:00 + 5 min = 9:05 a.m. c. 1:18 + 47 min: 18 + 47 = 65 min = 1 hr 5 min. End time: 2:05 p.m.
  3. Start times: a. 5:00 minus 45 minutes = 4:15 p.m. b. 8:15 minus 1 hour = 7:15; 7:15 minus 30 min (minus 15 to 7:00, minus 15 to 6:45) = 6:45 p.m.
  4. Experiment duration: 9:48 to 10:00 = 12 minutes. 10:00 to 10:32 = 32 minutes. Total = 12 + 32 = 44 minutes.
  5. Practice comparison:
  6. Oliver: 4:15 to 5:15 = 1 hour; 5:15 to 5:30 = 15 min -> 1 hour 15 minutes (75 minutes).
  7. Leo: 4:30 to 5:30 = 1 hour; 5:30 to 5:40 = 10 min -> 1 hour 10 minutes (70 minutes). Oliver's soccer practice is longer by 5 minutes.