Time: Calculations around the clock

The bread should be in the oven for 45 minutes. It’s 11:50, so the bread will be done at… 11:95! No, Leon. This is not correct. No, this is not correct… But… when will it be ready then?

When you add two times together, you have to think somewhat differently compared to when you add ordinary numbers. One way to think about it is to first count to the next full hour, when the minutes switch to zero. How many minutes have passed then? We started at 11:50, so when it’s 12 o’clock, ten minutes have passed. And the bread needs 45 minutes in the oven.

That leaves 35 minutes. The time will be 12:35 when the bread is done. Another way to calculate is like Leon did when he arrived at “11:95”. The minutes switch to zero when they reach 60, so 11:95 does not exist. But you can take 60 of the 95 minutes and convert them into one hour.

That leaves you with 35 minutes. The time “11:95” doesn’t exist. Instead Leon’s bread will be done at 11 plus 1 hour plus 35 minutes. 12:35. Here’s another calculation: A train ride starts at 22:40 at night and takes 8 hours and 25 minutes.

What time will the train arrive? We can split the travel time in this way: It is 20 minutes to the next full hour, when the minutes switch to zero. By then, it’s 23:00. Then we have another hour until a new day starts, when the hours switch to zero. So, we have been travelling for 1 hour and 20 minutes by midnight, when the clock strikes 00:00.

How much time do we have left to go? The whole train ride takes 8 hours and 25 minutes. If we remove the 1:20 that has already passed, we have 7 hours and 5 minutes left of the journey after midnight. The train will arrive at 07:05. With the second way of calculating, you first add the hours, and then the minutes.

The starting time was 22:40, plus the travel time which was 8:25. This gives the “time” 30:65. The hours switch to zero when the clock strikes 24. Then, it’s 6 hours to 30. This means that 30 hours is the same as one day and 6 hours.

The minutes switch to zero when they reach 60. This means that 65 minutes is the same as one hour and 5 minutes. So, the “time” 30:65 equals 1 day, 6 hours, 1 more hour, and 5 minutes. Or, 1 day, 7 hours and 5 minutes. The train arrives at 07:05, the day after the journey started.

What if there are even more minutes involved? If it’s 10:41, what’s the time 343 minutes later? Just adding the minutes would give the “time” 10:384. 384 minutes, how many hours is this? Well, there are 60 minutes in every hour, so divide 384 by 60.

That’s 6 hours and a remainder. 6 hours equals 360 minutes. 384 minus 360 equals 24, so the remainder is 24. This means that 384 minutes is 6 hours and 24 minutes. The “time” 10:384 is the same as 10 hours plus six hours plus 24 minutes.

343 minutes after 10:41 is 16:24. And now the bread is done. So soon? Right on time!