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Number - Time zones, clocks, and timetables

Grade 10IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The 24-hour clock system uses a four-digit format from 00:0000:00 (midnight) to 23:5923:59. To convert PM times to 24-hour format, add 1212 to the hours (except for 12:00 PM).

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Time is a base-60 system (sexagesimalsexagesimal). 11 hour = 6060 minutes and 11 minute = 6060 seconds. Calculations like 1.51.5 hours represent 11 hour and 3030 minutes, not 11 hour and 5050 minutes.

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When calculating time intervals, it is often easier to 'bridge' to the next whole hour. For example, to find the time from 08:4508:45 to 11:1511:15, calculate 08:4508:45 to 09:0009:00 (1515 mins), 09:0009:00 to 11:0011:00 (22 hours), and 11:0011:00 to 11:1511:15 (1515 mins), totaling 22 hours 3030 minutes.

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Time Zones are based on Longitude. The world is divided into 2424 time zones. Since the Earth rotates 360∘360^\circ in 2424 hours, every 15∘15^\circ of longitude represents a 11-hour difference.

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Greenwich Mean Time (GMT) or Universal Coordinated Time (UTC) is the reference point (0∘0^\circ longitude). Locations East of GMT are ahead (++) and locations West of GMT are behind (−-).

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Travel calculations must account for time zone shifts: Arrival Time (Local)=Departure Time (Local)+Travel Duration±Time Zone Difference\text{Arrival Time (Local)} = \text{Departure Time (Local)} + \text{Travel Duration} \pm \text{Time Zone Difference}.

📐Formulae

1 day=24 hours1 \text{ day} = 24 \text{ hours}

1 hour=60 minutes1 \text{ hour} = 60 \text{ minutes}

Time Difference (hours)=Difference in Longitude15∘\text{Time Difference (hours)} = \frac{\text{Difference in Longitude}}{15^\circ}

Average Speed=DistanceTime\text{Average Speed} = \frac{\text{Distance}}{\text{Time}}

💡Examples

Problem 1:

A flight departs from London (UTC+0) at 22:4522:45 on Monday and arrives in Dubai (UTC+4) after a flight duration of 77 hours and 1515 minutes. What is the local time and day in Dubai upon arrival?

Solution:

Departure Time (UTC+0)=22:45\text{Departure Time (UTC+0)} = 22:45 Flight Duration=7h 15m\text{Flight Duration} = 7\text{h } 15\text{m} Arrival Time (UTC+0)=22:45+7h 15m=06:00 (Tuesday)\text{Arrival Time (UTC+0)} = 22:45 + 7\text{h } 15\text{m} = 06:00 \text{ (Tuesday)} Dubai Local Time=06:00+4 hours=10:00 (Tuesday)\text{Dubai Local Time} = 06:00 + 4\text{ hours} = 10:00 \text{ (Tuesday)}

Explanation:

First, add the flight duration to the departure time to find the arrival time in the original time zone. 22:45+722:45 + 7 hours is 05:4505:45 the next day; adding the remaining 1515 minutes gives 06:0006:00. Finally, adjust for the Dubai time zone by adding 44 hours.

Problem 2:

Calculate the duration of a train journey that starts at 08:5208:52 and ends at 13:1513:15.

Solution:

Borrow 11 hour (6060 minutes) from 1313 to make the subtraction possible: 13:1513:15 becomes 12:7512:75. 12:75−08:5204:23\begin{array}{r} 12:75 \\ - 08:52 \\ \hline 04:23 \end{array} The duration is 44 hours and 2323 minutes.

Explanation:

To subtract times where the minutes of the end time are less than the start time, borrow 6060 minutes from the hour column. 1515 minutes becomes 7575 minutes, and 1313 hours becomes 1212 hours. Then subtract normally.

Problem 3:

City A is at longitude 30∘30^\circ E and City B is at 45∘45^\circ W. If it is 14:0014:00 in City A, what time is it in City B?

Solution:

Total Longitude Difference=30∘+45∘=75∘\text{Total Longitude Difference} = 30^\circ + 45^\circ = 75^\circ Time Difference=75∘15∘=5 hours\text{Time Difference} = \frac{75^\circ}{15^\circ} = 5 \text{ hours} City B Time=14:00−5 hours=09:00\text{City B Time} = 14:00 - 5 \text{ hours} = 09:00

Explanation:

Since one city is East and the other is West, add the longitudes to find the total difference. Divide by 15∘15^\circ to find the hour difference. Since City B is further West than City A, subtract the time difference from City A's time.