Math Detours · Grade 5 · Connections · 1

What time is it in Tokyo?

The Earth turns once in 24 hours, so the world is cut into 24 time zones. Adding and subtracting hours, across midnight.

Name ____________________Date ____________

Tonight's idea

The Sun can only light half the Earth at once. When it is midday for you, it is the middle of the night on the far side of the world.

The Earth turns once every 24 hours. So the world is cut into 24 strips called time zones, one for each hour. Places to the east meet the morning Sun first, so their clocks are ahead. Places to the west are behind.

Los Angeles 4 am 8 New York 7 am 5 London noon 0 Cairo 2 pm 2 Tokyo 9 pm 9 Sydney 11 pm 11 ← hours behind London hours ahead of London →
Clocks around the world at noon in London, in January. The number under each city is its gap from London in hours.

Ahead: add the hours. Behind: take them away. If you cross midnight, the day changes too.

Real zones bend to follow the borders of countries. Many places also move their clocks by an hour in summer, so the gaps can change during the year. This sheet uses the January gaps in the picture.

Watch one: 6 pm on Tuesday in London

Tokyo is 9 hours ahead, so add 9. Do it in two steps. From 6 pm, 6 hours takes you to midnight. That leaves 3 more.

\[\text{6 pm Tuesday} + 6 \text{ hours} = \text{midnight}, \qquad \text{midnight} + 3 \text{ hours} = \text{3 am Wednesday}.\]

New York is 5 hours behind, so take away 5. That gives 1 pm on Tuesday.

It is one moment, with three clock times on two different days.

Your turn

Use the gaps in the picture for every question.

  1. It is 10 am on Monday in London. What time is it in (a) Cairo, (b) New York, (c) Tokyo?
  2. It is 8 pm on Friday in London. Give the time and the day in (a) Tokyo, (b) Sydney, (c) Los Angeles.
  3. (a) Tokyo is 9 hours ahead of London. New York is 5 hours behind London. How many hours is Tokyo ahead of New York? (b) It is 3 pm on Monday in New York. What time and day is it in Tokyo?
  4. Mia lives in London. Her cousin Sam lives in Sydney. Each of them is awake from 7 am to 9 pm by their own clock. (a) When it is 8 am for Mia, what time is it for Sam? (b) Find all the London times when Mia can phone and both are awake.

Stretch: the short afternoon

A plane leaves Tokyo at 1 pm on Tuesday. It flies for 12 hours and lands in London. What does the clock in London say? The clocks seem to say the trip took less than 12 hours. Explain.

Answers

  1. (a) 12 noon. (b) 5 am. (c) 7 pm. All on Monday.
  2. (a) 5 am on Saturday: 4 hours to midnight, then 5 more. (b) 7 am on Saturday. (c) 12 noon on Friday.
  3. (a) \(9 + 5 = 14\) hours. Going from New York to Tokyo you pass London on the way. (b) 3 pm plus 14 hours: 9 hours to midnight, then 5 more. It is 5 am on Tuesday.
  4. (a) 7 pm, the same day. (b) Sam's clock is 11 hours ahead. From 7 am to 10 am in London it is 6 pm to 9 pm for Sam, so that works. After 10 am in London Sam is asleep. Sam wakes at 7 am, which is 8 pm the evening before in London. So 8 pm to 9 pm works too. Two windows: 7 am to 10 am, and 8 pm to 9 pm.

Stretch. At take-off it is 1 pm in Tokyo, so it is 4 am on Tuesday in London. Twelve hours later it is 4 pm on Tuesday in London. Tokyo's clock said 1 pm at the start and London's says 4 pm at the end: only 3 hours apart. The flight really took 12 hours. The other 9 hours are the gap between the two clocks.

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