What are start and end times?
Start time is the moment an activity begins. End time is the moment an activity finishes. The elapsed time is the amount of time that passes from the start time to the end time.
- A soccer practice starts at 4:15 p.m. and ends at 5:45 p.m.
- The start time is 4:15 p.m. The end time is 5:45 p.m.
- The elapsed time is 1 hour and 30 minutes.
When you know any two of these three pieces of information—start time, end time, and elapsed time—you can often find the third one.
Reading a clock and writing time correctly
An analog clock has an hour hand and a minute hand. The hour hand shows the hour. The minute hand shows how many minutes after the hour have passed. When writing time, use a colon between the hour and the minutes, such as 3:40. Use a.m. for times from midnight to noon and p.m. for times from noon to midnight.
- 7:05 a.m. means 5 minutes after 7 in the morning.
- 2:30 p.m. means 30 minutes after 2 in the afternoon.
- 12:00 p.m. is noon. 12:00 a.m. is midnight.
Do not write 3.40 for a time. A period is used for decimals, but a colon is used for time.
Counting minutes on a clock
Each number on a clock is 5 minutes apart. You can skip-count by fives to find the minutes: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60. There are 60 minutes in 1 hour.
- The minute hand on 3 shows 15 minutes.
- The minute hand on 6 shows 30 minutes.
- The minute hand on 9 shows 45 minutes.
Half past means 30 minutes after the hour. Quarter past means 15 minutes after the hour. Quarter till means 15 minutes before the next hour.
Finding elapsed time by counting forward
To find elapsed time, count forward from the start time to the end time. You can count by hours first, then by minutes. This method works well when the start and end times are close together.
- Start: 9:20 a.m. End: 10:05 a.m.
- From 9:20 to 10:00 is 40 minutes.
- From 10:00 to 10:05 is 5 minutes.
- Elapsed time: 40 + 5 = 45 minutes.
It is often easier to count up to the next hour first, then count the remaining minutes.
Finding elapsed time by subtracting
When both times are on the same side of noon, you can subtract the start time from the end time to find the elapsed time. Subtract the minutes first. If needed, regroup 1 hour as 60 minutes.
- End: 3:35 p.m. Start: 1:10 p.m.
- 35 minutes − 10 minutes = 25 minutes.
- 3 hours − 1 hour = 2 hours.
- Elapsed time: 2 hours and 25 minutes.
If the end minutes are less than the start minutes, regroup 1 hour from the end time as 60 minutes before subtracting.
Finding an end time
To find an end time, add the elapsed time to the start time. Add the hours first, and then add the minutes. If the minutes add up to 60 or more, regroup 60 minutes as 1 hour.
- Start: 10:20 a.m. Elapsed time: 1 hour 50 minutes.
- 10:20 a.m. + 1 hour = 11:20 a.m.
- 11:20 a.m. + 50 minutes = 12:10 p.m.
- End time: 12:10 p.m.
After 11:59 a.m., the next time is 12:00 p.m. After 11:59 p.m., the next time is 12:00 a.m. Be careful when you cross noon or midnight.
Finding a start time
To find a start time, subtract the elapsed time from the end time. Subtract the hours first, and then subtract the minutes. If you need more minutes, regroup 1 hour as 60 minutes.
- End: 4:45 p.m. Elapsed time: 2 hours 15 minutes.
- 4:45 p.m. − 2 hours = 2:45 p.m.
- 2:45 p.m. − 15 minutes = 2:30 p.m.
- Start time: 2:30 p.m.
You can check your answer by adding the elapsed time back to the start time. The result should be the end time.
Using a number line for time
A number line can help you see the jumps between times. Write the start time on the left and the end time on the right. Then make jumps for hours and minutes until you reach the end time.
- Start: 1:15 p.m. End: 3:00 p.m.
- Jump 45 minutes from 1:15 p.m. to 2:00 p.m.
- Jump 1 hour from 2:00 p.m. to 3:00 p.m.
- Elapsed time: 1 hour 45 minutes.
Label each jump clearly. This helps you avoid losing track of the hours and minutes.
Solving word problems about time
Time word problems ask you to find a start time, an end time, or an elapsed time. Read the problem carefully. Look for clue words such as starts, ends, lasts, from, and to. Decide what you already know and what you need to find.
- Maya starts reading at 6:40 p.m. She reads for 35 minutes. When does she stop?
- 6:40 p.m. + 20 minutes = 7:00 p.m.
- 7:00 p.m. + 15 minutes = 7:15 p.m.
- Maya stops reading at 7:15 p.m.
After you solve a problem, ask yourself if the answer makes sense. For example, if an activity starts in the afternoon and lasts 2 hours, the end time should also be in the afternoon or early evening.
Time across noon and midnight
Times can cross from a.m. to p.m. or from p.m. to a.m. When this happens, count forward carefully. The clock shows 12:00 at noon and at midnight, but the labels a.m. and p.m. change.
- Start: 11:30 a.m. Elapsed time: 45 minutes.
- 11:30 a.m. + 30 minutes = 12:00 p.m.
- 12:00 p.m. + 15 minutes = 12:15 p.m.
- End time: 12:15 p.m.
Twelve o’clock noon is written 12:00 p.m., and twelve o’clock midnight is written 12:00 a.m.
Choosing the right strategy
Different time problems call for different strategies. Counting forward works well for short elapsed times. Subtracting works well when both times are given. Adding elapsed time works well when you need to find an end time. Subtracting elapsed time works well when you need to find a start time.
- Find elapsed time: subtract or count forward.
- Find end time: add elapsed time to start time.
- Find start time: subtract elapsed time from end time.
Always write the units. Minutes and hours are different units, just like inches and feet. Labeling your answer helps you check that it is reasonable.
Checking your work
You can check a time answer by working backward. If you found an end time, subtract the elapsed time from your answer. You should get the start time. If you found a start time, add the elapsed time to your answer. You should get the end time.
- Start: 8:10 a.m. Elapsed time: 1 hour 25 minutes. End: 9:35 a.m.
- Check: 9:35 a.m. − 1 hour = 8:35 a.m.
- Check: 8:35 a.m. − 25 minutes = 8:10 a.m.
- The answer checks out.
A good mathematician always checks the answer. Checking helps you catch small mistakes with regrouping or with a.m. and p.m.
Time vocabulary to remember
Start time: when an activity begins. End time: when an activity finishes. Elapsed time: how long an activity lasts. a.m.: from midnight to noon. p.m.: from noon to midnight. Regroup: to rename 1 hour as 60 minutes or 60 minutes as 1 hour.
- Start time: 7:00 a.m.
- End time: 8:30 a.m.
- Elapsed time: 1 hour 30 minutes.
Use these words when you explain your thinking. Clear math language helps others understand your solution.
Common Core alignment: CCSS.MATH.CONTENT.4.MD.A.2 – Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money.
Notes for teachers
This resource is designed to provide clear explanations, examples, and practice for learners of different needs and levels of support. It may be used for whole-class instruction, guided practice, independent learning, review, homework, or additional reinforcement at home.