Calculating with time

The train leaves at 14:47 and the journey takes 35 minutes: when do you arrive? The cake needs 50 minutes in the oven and you want to eat at 18:00: when does it have to go in? You answer questions like these every day, and yet even adults get them wrong. The reason is simple: with clock times, calculating works differently than with ordinary numbers. Here you'll learn why that is and how a few jumps let you solve any time problem with confidence.

Why 60 and not 100?

An hour has 60 minutes and a minute has 60 seconds. We inherited this division from the Babylonians, who calculated in base 60 around 4000 years ago. And 60 is a clever choice: it divides evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, which is why half an hour, a quarter of an hour and a third of an hour are all whole numbers of minutes. For calculating, though, it means the carry happens at 60, not at 100. 45 minutes plus 30 minutes make 75 minutes, and that is 1 hour and 15 minutes. And watch out with decimals: 1.5 hours is 90 minutes, not 150.

Jumping via the full hour

The best trick for clock times works like a number line: you jump via the next full hour. A film starts at 19:40 and runs for 100 minutes. First you jump 20 minutes to 20:00, then 80 minutes remain, which is 1 hour and 20 minutes: the film ends at 21:20. You find elapsed time the same way. From 9:35 to 11:10 you jump 25 minutes to 10:00, then 1 hour to 11:00, then 10 more minutes: 1 hour and 35 minutes in total. That is how you solve the train question from the beginning too: from 14:47 it is 13 minutes to 15:00, then 22 more minutes, so you get there at 15:22. The full hour is your stopover, just like the round 10 in ordinary arithmetic.

Planning backwards

Often you know the end time and need the start: the bus leaves at 8:15 and you need 25 minutes to reach the stop. So you jump backwards, first 15 minutes to 8:00, then 10 more minutes: you have to leave by 7:50 at the latest. Calculating backwards is nothing but calculating forwards in the other direction, and the full hour is still your stopover. That also settles the cake question from the beginning: dinner at 18:00, 50 minutes of baking time, so you jump back 50 minutes. The cake has to go into the oven by 17:10 at the latest.

Converting units

Whenever you convert units, 60 is your friend: hours times 60 give minutes, minutes times 60 give seconds. So 2 hours and 30 minutes are exactly 150 minutes, and 2 minutes are 120 seconds. Going the other way, you divide: 180 minutes divided by 60 is 3 hours, and if something is left over, that remainder is the extra minutes. That is how 95 minutes become 1 hour and 35 minutes. With the jump via the full hour and the 60 in mind, no time problem is a puzzle anymore.