Alpha's Adventures in Mathematics

Volume One: Chapter Five


Alpha is off to the airport with Carlos, Henry, EK and June, along with some other lucky pups, to fly to their forever homes!

Alpha is nervous about the trip but is looking forward to meeting his new family and finding out about all the math along the way! So let's go... 

Chapter 5: Arriving at the Airport

After a long van ride, 2 hours, we arrived at the airport!

The first thing I saw was people, everywhere! With bags and suitcase, all rushing to get to their flights. 

The next thing I saw were giant boards listing all the flights coming and going. Plus, there were clocks on the walls ticking away different times in different city from here to Kalamazoo. 

But why did all the clockshave different times? This called for closer inspection so I weaved through all the people to get a better view.

It was there that I overheard a daughter and mother talking about clocks and time zones.

Hey Mom, check out the clocks! Did you know there are 37 different local times used around the world?

That’s nice dear... where is our flight?

It’s so that people around the world have a common time to refer to for things like breakfast or lunch or work hours. 

Wait, did we eat breakfast this morning?

Most time zones are set with the sun so they are an hour apart.

No, I definitely think we forgot to eat breakfast. We’ll have to order snacks on the plane.

The Earth spins on an axis, so the sun comes up at different times in different cities.

That’s all fascinating sweetie, but we’re going to miss our plane.

Not if we were in Alaska! We’d actually be 18 hours early for our flight and it would still be yesterday!



Yeah, time zones are weird. In fact, when we land it will be the exact same time, and day, as when our plane took off from here.

Neat, huh?

That’s pretty cool.

But we really have to go, because we aren’t in Alaska. We’re here in Seoul and they’re calling us to board.

Come on!

As the little girl and her mother hurried off to the plane, I started thinking about what she had said. How can a plane take off and land at the same time and day that it departed?

She had said it was because of the way the Earth spins, so maybe that would help me figure it out.

It takes 24 hours for the Earth to turn around one full time, meaning there are 24 hours between sunrises each day (or between sunsets). If we divided the Earth up into 24 equal pieces then as the sun moved across the sky for each of those pieces it would look the same as the piece that came before an hour earlier.

So this must be what time zones do; they break the Earth up into pieces.  

From Pam

Even though there are 24 hours in a day there are actually more than 24 time zones (there are 37 local time zones to be exact). This is because some places in the world have divided their time zone into 30 or 45 minutes instead of an hour, and other places made their time zones different so a city or town wouldn't be cut in half by two different time zones. Some places in the world also use Daylight Savings Time, which adds an hour in fall and takes one away in spring, while other places don't.

The reasons for different times zones can be quite complicated, so, to help Alpha, we’re going to create a simplified globe with only 24 time zones (one for each hour of the day).

Explore More

You can learn more about time zones and local time zones here

You can also explore time zones using this neat interactive map (check out the box at the bottom where you can type in the name of any city or country and find out what time zone it's in)

This meant that if I wanted to find out what the time was in another part of the world I would need to build a time zone line.

Help Alpha

Alpha wants to build a simple time zone line to see what time it is in different parts of the world. To do this he needs to know a few facts first: 

  • Greenwich Mean Time (GMT) is considered to be 0 hours on the time line
  • If we move west, the direction the sun moves, we subtract 1 hour for every time zone we pass through
  • If we move east, we add 1 hour for each time zone

For example:

  • Seoul is 9 time zones east of London. So, if we want to know the local time in Seoul, we take whatever time it is in London and add 9 hours to it 
  • Toronto, however, is 5 time zones west of London. So we take whatever time it is in London and subtract 5 hours from it to find the local time in Toronto.

Let's try: 

  • In London it is 6:00am.
  • This means in Seoul it is 6:00 + 9 hours = 15:00 (or 3:00pm).
  • And in Toronto it is 6:00 - 5 hours = 1:00 (or 1:00am)

From Pam

Sometimes, when doing calcuations with time zones, it is easier to use 24-hour time instead of 12-hour (which uses am and pm).

Here is an easy chart to switch between 12- and 24-hour time: 

12-hour (am/pm) 24-hour
0:00 am 00:00 midnight
1:00 am 01:00
2:00am 02:00
3:00am 03:00
4:00am 04:00
5:00am 05:00
6:00am 06:00
7:00am 07:00
8:00am 08:00
9:00am 09:00
10:00am 10:00
11:00am 11:00
12:00pm 12:00 noon
1:00pm 13:00
2:00pm 14:00
3:00pm 15:00
4:00pm 16:00
5:00pm 17:00
6:00pm 18:00
7:00pm 19:00
8:00pm 20:00
9:00pm 21:00
10:00pm 22:00
11:00pm 23:00
12:00pm 24:00 midnight

You may notice that both 24:00 and 00:00 are midnight.

00:00 is used to say the start of one day and 24:00 is used for the end of another. 

So 24:00 on Tuesday is the exact same time as 00:00 on Wednesday. 

Try At Home

Now that we know how time zones work and how to break up the world into different zones, we're going to create two different types of time zone lines.

The first is to draw a simple line that looks like this:

Important Note: the -12 and +12 time zones are actually the same

Now, on your time line you can mark the following: 0 = GMT (London), -5 = EST (Toronto) and 9 = JST (Seoul). You can then use the time zone list here or the map here to fill in other time zones if you like.

Bonus: find your city on the map and put in the time zone you live in on the line as well.

The second time zone line will use the map found here (or any other map of the world or globe you like). Divide the map into 24 time zones just like you did on your time zone line.

Now we can use the time zone line, and the map, to help Alpha further in his adventure. 



Ok. So I'm going to assume for now there are 24 time zones. I’m currently in Seoul where it’s 7:00 a.m. on March 4th. I decided to start with an easy calculation to get my brain warmed up. I wanted to know what time it was in Sydney, Australia. I knew that Sydney was in time zone +10 on my time zone line, and Seoul is in time zone +9. So this meant that Sydney was one hour ahead of Seoul. This gave me 07:00 + 1 hour = 08:00 hours in Sydney. 

Alright, time for a more challenging one. Since Seoul is almost at the far east end of the time zone line there aren't too many places east of it. Meaning most time zones are going to be west of Seoul, meaning we're going to have to move west on our time zone line and subtract hours instead of adding them. 

So, let’s say I’m going to Dubai.

If Dubai is in time zone +4 and Seoul is in time zone +9 and we are moving west to get there we calculate how many time zones we move through to get there. 

This gives us 9 - 4 = 5 time zones, so 5 hours.  

Now to find the local time in Dubai we take the local Seoul time (07:00) minus the number of hours difference (5). This gives us 07:00 - 5 = 02:00 or 2:00 a.m. on March 4th. 

Ok, so now for the tricky part...

I can see from the departure board at the airport that the flight to Dubai is 10 hours long.

I know the time in Dubai right now is 02:00. So 10 hours from now in Dubai gives me 02:00 + 10 = 12:00 (or noon) in Dubai on March 4th. This means, if I was going to Dubai, I’d actually be landing only 5 hours (local time) after I took off from Seoul. Kind of like like I gained 5 whole hours. Neat!

But I’m not going to Dubai, I’m going to Toronto. I wonder what time will it be when I arrive there?

Help Alpha

Ok, so Alpha wants to calculate the time it will be in Toronto when he lands... let's help him out.

Here's what we know: 

Toronto is in time zone -5
Seoul is in time zone +9
The flight from Seoul to Toronto is 14 hours 

Use your time zone line and count how many time zones the flight will pass through to get from +9 to -5. This gives you the number of hours difference.

Now, remember, Toronto is west of Seoul so we have to subtract the number of time zones to get the local time in Toronto. 

Ok, ready, here we go... 

Time Zone Difference 

There are three ways to do this:

  • count the number of spaces on the time zone line
  • calculate the difference from Seoul to London (the 0 on the time line) and then add it to the difference from London to Toronto.
  • use integer math to calcuate it 

The difference from Seoul to London is 9, from London to Toronto is 5, so 9 + 5 = 14

Using integer math we can subtract the two numbers from each other to give: +9 - (-5) = 9 + 5 = 14 (in integer math two -'ves give +'ive) 

No matter which way we calcualte it though we find there is a 14 hour time difference between Seoul and Toronto.  

So when it's 07:00 on March 4th in Seoul it's 07:00 - 14 hours = 17:00 on March 3rd in Toronto. 

When Will We Land 

Ok, so if the plane flight is 14 hours long and we're going through 14 time zones, what time will it be when we arrive in Toronto. 

If it's 17:00 on March 3rd in Toronto, 14 hours from now it will be...

07:00 on March 4th! 

That's the exact same time we left Seoul! 

By the magic of time zones Alpha travelled halfway across the world and didn't even lose a day of time!


Important Note: our calculations do NOT take into account daylight savings time! If they did the time would be different by an hour depending on the time of year.

From Pam

Time zones can be tricky and frustrating, so don't worry if it takes a little while to figure them out, even Alpha and I had to look up some information to make sure we got it right!

Using a time zone map or line can be very helpful, and the internet can also help converting from one time zone to another. 

One more, super bonus trick, to time zones includes what is called the International Date Line. 

We simplified the problem for you to make the flight from Seoul to Toronto fly west. In truth though, the flight from Seoul to Toronto goes the other way. They fly east and cross the International Date Line. 

This means that when Alpha was on the plane he flew through 3 time zones (from +9 to +12) on March 4th. He then crossed over the date line into March 3rd. He then continued on through another 7 time zones to arrive in Toronto at 07:00 on March 4th. 

When you cross over the date line the time remains the same but the date goes back one. Meaning Alpha would have crossed over the date line around


Wait! But you said it was a 14 hour flight, there's only 10 time zones that way... 

You're right, this is because, going this way, it takes 14 hours to cover 10 time zones, meaning the plane crosses each time zone every 84 minutes. 

It makes the calculation a bit harder but you can still follow the pattern to see that the plane still lands in Toronto at 07:00 on March 4th.

Note: I am hoping to make a video soon to explain this but in the meantime try using your time line and pretending that you are sitting on the plan. Every time you cross into a new time zone your watch automatically updates to the new LOCAL time for where the plane is. Remember that it takes 84 minutes to cross from one time zone to the next so start by updating your time to just before you cross the line and then right after. 

Let's Try It Together

You get on the plane in Seoul and your watch reads 07:00. 

84 minutes later you cross into the next time zone. Just before you cross your watch will read 07:00 + 84 minutes = 08:24. 

As soon as you cross the line your watch now reads 09:24. 

Repeat this for the next time zone to get 09:24 + 84 minutes = 10:48. Cross the time zone line and get 11:48.  

The next one is the same: 11:48 + 84 = 13:12 + 1 time zone (tz) = 14:12

Now it gets tricky as we cross the Date Line:
14:12 + 84 = 15:36 + 1 time zone = 16:36
16:36 - 1 day = 16:36 March 3rd (not the 4th)

Now it becomes a bit more straight forward: 

The next few time zones look like this: 

16:36 + 84 = 18:00 + 1 tz = 19:00
19:00 + 84 = 20:24 + 1 tz = 21:24
21:24 + 84 = 22:48 + 1 tz = 23:48

Now another tricky bit:

23:48 + 84 = 01:12 + 1 tz = 02:12 (but it's now March 4th)

We're now at 8 time zones, only 2 more to go...

02:12 + 84 = 03:36 + 1 tz = 04:36
04:36 + 84 = 06:00 + 1 tz = 07:00

There we go, 07:00 on March 4th the plane lands, the same time it took off from Seoul...

Whew! And great work...

Try At Home

Use your time line, map and the links provided to explore time zones around the world. 

You can also look up flight times and use Google Maps to show what route planes take to get to different parts of the world. 

Explore travelling both east to west and west to east and see how time zones change.

You can also explore more about the other special time zones that make up the 13 time zones, to give us 37 total time zones. 

Pick some places you've been, or would like to go, and try to figure out the local time and how long it would take to get there by plane. 

Explore the world through time zones and let us know of any amazing places you find by emailing us (with your parents permission) at

Whew! That was a lot of math... I was exhausted. But before I had a chance to rest, I heard June calling me. So I ran back to the group and got ready to board our flight. 

Toronto, here we come!

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Learn more on our Give Alpha a Treat page...

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