Time zones

Why this exists

Baraka lives in Nairobi, in Kenya. Hoku lives in Honolulu, in Hawaii. Mitra lives in Kolkata, in India. They are pen pals, and they want to talk on a video call. When Baraka says “let’s call at 19{:}00”, he means 19{:}00 on his clock. On Hoku’s clock it is a very different time. So how do they find a time that works for everyone?

The reason is the sun. The Earth turns once a day, from west to east. So the sun rises in the east and seems to travel across the sky toward the west. Noon at a place is meant to be the time when the sun is highest in the sky there. When the sun is highest over Nairobi, it has not yet climbed high over places to the west, and it has already passed its highest point for places to the east. So noon cannot happen everywhere at once. Each place needs its own clock time, and the world needs a plan so that those clocks fit together.

That plan is the system of time zones. These times are written in the twenty-four hour way, which gives each hour of the day its own number from 0 to 23 (Twenty four hour time and crossing midnight).

Definition

A time zone is a region where everyone sets their clocks to the same time.

Every zone is measured from one reference clock called Coordinated Universal Time, or UTC for short. Think of UTC as the clock the whole world agrees to count from. In winter, the clocks in London show UTC exactly.

A zone’s offset is how many hours its clocks are ahead of UTC or behind it. “UTC +3” means 3 hours ahead of UTC. “UTC -5” means 5 hours behind UTC.

Most offsets are a whole number of hours. A few are not: India is \displaystyle 5\frac{1}{2} hours ahead and Nepal is \displaystyle 5\frac{3}{4} hours ahead.

Many places move their clocks forward one hour in summer, called daylight saving time. That changes their offset for part of the year. This lesson sets it aside and uses standard time, the winter offsets, which are these:

Intuition

Day 1: zones on a number line

Lay the offsets on a number line, with UTC at 0. Behind goes to the left, ahead goes to the right.

Now the gap between two places is just a distance on the line. From New York at -5 to Nairobi at +3 is 5 hours to reach 0 and 3 more, so 8 hours. Nairobi is to the right, so Nairobi is 8 hours ahead. When it is 9{:}00 in New York, it is 17{:}00 in Nairobi.

Going to a place further right, you add the gap. Going further left, you subtract it.

Why is east ahead? The sun reaches its highest point over eastern places first, so their noon comes first. Their clocks have to be ahead to show noon at the right moment.

Adding hours can carry you past midnight. The clock then starts again from 0{:}00, and the day changes. Subtracting can carry you back before midnight, into the day before. A time line drawn across midnight shows both.

Day 2: parts of an hour, flights, and the date line

An offset of \displaystyle 5\frac{1}{2} hours is 5 hours 30 minutes, and \displaystyle 5\frac{3}{4} hours is 5 hours 45 minutes, because \displaystyle \frac{1}{2} of 60 minutes is 30 and \displaystyle \frac{3}{4} of 60 is 45. So India’s clocks show a time ending in 30 when London’s show a whole hour, and Nepal’s clocks run 15 minutes ahead of India’s.

A flight across zones has two kinds of time in it. The elapsed time, how long you are in the air, is the same on every clock in the world (Elapsed time). The clock time at the airport you land at also includes the gap between the two zones.

Keep going east across the zones and you keep adding hours. Somewhere the world has to say where one calendar day ends and the next begins. That place is the International Date Line. It roughly follows the line of longitude at 180 degrees, halfway around the world from London, with bends in places. Just west of the line the date is one day later than just east of it. Tokyo is west of the line and Honolulu is east of it.

Results

Worked examples

Examples 1 to 4 are for day 1: whole-hour gaps, and crossing midnight. Examples 5 to 7 are for day 2: parts of an hour, a flight, and the date line.

Boundaries

• Daylight saving time is set aside here. Many places move their clocks forward an hour in summer, and not all on the same dates. So the gap between two places can change during the year. The method still works with the summer offsets, but the numbers in this lesson are the winter ones.
• Zones are set by people, not by the sun alone. Each country chooses its offset by law, and it can choose to change it. Borders follow countries and states rather than straight strips. China, a wide country, uses a single zone, 8 hours ahead of UTC.
• Noon on the clock is only roughly when the sun is highest. Inside one zone, places in the east of the zone see the sun highest at an earlier clock time than places in the west, so it cannot be exactly 12{:}00 everywhere in the zone.
• Elapsed time never changes with the zone. A 9 hour flight is 9 hours on every clock. Only the clock reading at each end depends on where you are.
• A clock time alone does not name a moment. “10{:}00” means a different moment in each zone, so a call time has to say which zone’s clock it uses.

Where this goes next

Changing a time from one zone to another is a unit problem in disguise: hours and minutes have to be regrouped just as in Multi-step problems with unit conversions, where a trip’s legs in hours and minutes are added up. Days, hours and the calendar fit together in Units of time and Calendars and dates. Later, the offsets become signed numbers, with behind as negative and ahead as positive (Integers). Then the gap between two zones is a subtraction of signed numbers, the way Rational numbers in real situations treats it with fractional offsets.

Exercises

Use the standard-time offsets in the table under Definition.

Day 1: whole-hour gaps and crossing midnight

1. It is 9{:}00 in London. What time is it in Nairobi?
2. It is 15{:}00 in Tokyo. What time is it in London?
3. It is 10{:}00 in Los Angeles. What time is it in New York?
4. It is 18{:}00 in New York. What time is it in Los Angeles?
5. How many hours apart are Honolulu and New York, and which one is ahead?
6. It is 7{:}00 in Honolulu. What time is it in London?
7. Baraka calls Hoku at 21{:}00 on Friday, Nairobi time. What time and day is it for Hoku?
8. It is 22{:}00 on Thursday in London. What time and day is it in Tokyo?
9. It is 23{:}00 on Sunday in Los Angeles. What time and day is it in London?
10. It is 4{:}00 on Wednesday in Tokyo. What time and day is it in New York?
11. It is 2{:}00 on Saturday in Nairobi. What time and day is it in Honolulu?
12. It is 15{:}00 on Monday in Honolulu. What time and day is it in Nairobi?

Day 2: parts of an hour, flights, and the date line

13. It is 12{:}00 in London. What time is it in India?
14. It is 20{:}00 on a Friday in New York. What time and day is it in India?
15. It is 9{:}00 in Nepal. What time is it in India, and what time is it in London?
16. Mitra’s clock in India reads 21{:}30. What time is it for Baraka in Nairobi?
17. It is 10{:}00 in Tokyo. What time is it in India?
18. Hoku flies home. Her plane leaves Tokyo at 21{:}00 on Sunday, Tokyo time, and the flight takes 7 hours. What time and day is it in Honolulu when she lands?
19. On another trip, Hoku’s plane leaves Honolulu at 10{:}00 and lands in Tokyo at 15{:}00 the next day, Tokyo time. How long was the flight?
20. Mitra wants to call Hoku at 8{:}00 on Monday, India time. What time and day is it for Hoku?
21. It is 12{:}00 on Saturday in Tokyo. What day and time is it in Honolulu?

Reasoning

22. Explain why a place to the east of you has its clocks set ahead of yours, not behind.
23. Suppose the whole world used one clock, UTC, with no zones. What would go wrong with the meaning of “noon”?
24. Imagine walking all the way around the world going east, setting your watch 1 hour ahead each time you enter a new whole-hour zone. When you get home, how far has your watch moved? Explain why the world needs a date line.
25. Mitra says: “To change London time to Nepal time I add 5 h 45 min, and to change it to India time I add 5 h 30 min. So Nepal is 15 minutes ahead of India, at every moment.” Explain why she is right.