Explainer: Adding and Subtracting Units of Time

In this explainer, we will learn how to measure time in hours, minutes, and seconds by using addition and subtraction and use this skill to solve word problems.

Because of the rotation of Earth around itself, we, Earth inhabitants, experience day/night cycles.

The duration of each cycle (made of one day and one night) is 24 hours and is called a day. Each hour (h) is made of 60 minutes (min) and each minute is made of 60 seconds (s).

Definition: Units of Time

One day is 24 hours long.

One hour is 60 minutes long.

One minute is 60 seconds long.

Now that we have this time division in mind, we are going to see how to reason to solve different questions. Let us start with adding two times.

Example 1: Adding Two Times Measured in Hours and Minutes

William puts a meatloaf in the oven at 11:18 am. Given that it needs 2 hours and 58 minutes to bake, at what time should he take it out of the oven?

Answer

Here, we need to add 2 hours and 58 minutes to 11:18 am. We could carry out a kind of column addition here. However, we can notice that 2 hours and 58 minutes are very close to three hours. (It is just two minutes less than 3 hours.) So, we first add 3 hours to 11:18, which gives 14:18 on a 24-hour digital clock. Now, two minutes earlier is 14:16. This time is in the afternoon, so it is 2:16 pm.

Our answer is that William should take his meatloaf out of the oven at 2:16 pm.

Example 2: Adding Two Times Measured in Hours, Minutes, and Seconds

Add 11 hours, 15 minutes, and 49 seconds to 6 hours, 46 minutes, and 33 seconds.

Answer

We want to add two durations in hours, minutes, and seconds. For this, we are going to carry out a “time addition,” remembering that 1 hour = 60 minutes and 1 minute = 60 seconds: 111549+64633hminshmins

In the first step, we add the seconds: 49+33=82s. This is more than 60 seconds, so we rename it as 60(1)+22smins, write down 22 s in the result, and carry over 1 minute. 111549+6463322hminshminss

In the second step, we add the minutes: 1+15+46=62min. We rename it as 60 min (1 h) + 2 min, write down 2 min, and carry over one hour. 111549+64633222hminshminsmins

Finally, we add the hours: 1+11+6=18hours. 111549+6463318222hminshminshmins

Our answer is 18 hours, 2 minutes, and 22 seconds.

We are going to look now at how to find a time elapsed between two different times.

Example 3: Finding the Time Elapsed between Two Given Times

Find the elapsed time from 2:43 pm to 8:28 pm.

Answer

The best way to approach this sort of question is to draw a time line and place the two times given, here 2:43 pm and 8:28 pm. We note that both these times are “pm” (for post meridiem), which means that they are between midday and midnight. The next step is to place the next hour following 2:43 pm, that is, 3 pm, and the last hour before 8:28 pm, that is, 8 pm, on the time line.

Once this is done, we simply need to find the minutes from 2:43 pm to 3 pm: it is how many minutes needed to be added to 43 to get 60. We find it is 17 minutes. Then, we work out how many hours elapsed between 3 pm and 8 pm, that is, 5 hours. And we find that the number of minutes between 8 pm and 8:28 pm is 28 minutes.

Finally, we add the three times together: 17 min + 5 hours + 28 minutes = 5 hours and 45 minutes.

The next question looks different, but we are going to see that it is in fact very similar to the previous example.

Example 4: Finding the Difference between Two Times Measured in Hours, Minutes, and Seconds

Determine the difference between 6 hours, 48 minutes, and 27 seconds and 3 hours, 33 minutes, and 13 seconds.

Answer

To find the difference between the two given times, we place them on a time line.

In the first stage, we place the next minute after the earlier time, that is, 3 hours and 34 minutes and then the next hour: 4 hours.

In a second stage, we place the last minute before the later time: 6 hours and 48 minutes and the previous hour: 6 hours.

Once this is done, we work out the number of seconds between 3 hours, 33 minutes, and 13 seconds and 3 hours and 34 minutes, which is the number of seconds that are added to 13 to get 60. We find that this is 47 seconds. Then, the time difference between 3 hours and 34 minutes and 4 hours is 26 minutes (check that 34+26=60). The time between 4 hours and 6 hours is 2 hours, that between 6 hours and 6 hours and 48 minutes is 48 minutes, and, finally, that between 6 hours and 48 minutes and 6 hours, 48 minutes, and 27 seconds is 47 seconds.

We simply add all the times together by adding the minutes together and the seconds together: 47+26+2+48+27=2+74+74.sminhminshmins

We rename 74 minutes as one hour and 14 minutes, and 74 seconds as one minute and 14 seconds. This gives 2+1+14+1+14=3+15+14.hhminminshmins

So, the difference between the two times is 3 hours, 15 minutes, and 14 seconds.

Example 5: Finding the Difference between Two Times in a Day

Determine the elapsed time from 9:37 pm to 4:11 am.

Answer

To find the time elapsed between the two given times, we place them on a time line.

In the first stage, we place the next hour after the earlier time, that is, 10 pm. In a second stage, we place the previous hour before the later time, that is, 4 am. We need to notice that the first time is in the afternoon, while the second time is the next morning.

Once this is done, we work out the number of minutes between 9:37 pm and 10 pm. We find that it is 23 minutes. (Remember, it is the number of minutes that, added to 37 minutes, gives 60 minutes.) The number of hours between 10 pm and 4 am the next day is 6 hours. And the number of minutes between 4 am and 4:11 am is 11 minutes.

Finally, we simply add the three times together. This gives 23+6+11=6𝑎𝑛𝑑34.minuteshoursminuteshoursminutes

The time elapsed from 9:37 pm to 4:11 am is 6 hours and 34 minutes.

Key Points

  1. One day is 24 hours long.
  2. One hour is 60 minutes long
  3. One minute is 60 seconds long.
  4. To add times, we can carry out a “column time addition,” remembering that 1 hour = 60 minutes and 1 minute = 60 seconds.
  5. To subtract times, it is useful to use a time line. We start with placing the time we need to subtract from the other time, and we look for the time we need to add to this time, so we can get the other one, adding seconds first to reach the next full minute, then adding minutes to the next full hour, then adding hours to the next full day (if necessary), then adding the number of days, then hours, then minutes, and then seconds to reach the second time. All the times added to the first time is the difference between the second time and the first time.

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