Open Math›Year 11›Mathematics Standard›Time and location›Latitude and longitude

Latitude and longitude

Use latitude and longitude to identify locations and calculate time differences between places using the rule that 15° of longitude equals 1 hour.

Worked examples

Reading latitude and longitude coordinates

Straightforward

Problem

Buenos Aires, Argentina, is located at approximately

34°\text{S},\ 58°\text{W}

. (a) In which hemisphere (north or south) is Buenos Aires? (b) Is Buenos Aires east or west of the Prime Meridian? (c) State the latitude as a positive number of degrees.

Read the latitude coordinate and identify the hemisphere.

The latitude is

34°\text{S}

. The letter S indicates south of the equator, so Buenos Aires is in the Southern hemisphere.

Read the longitude coordinate and identify the direction from the Prime Meridian.

The longitude is

58°\text{W}

. The letter W indicates west of the Prime Meridian (

0°

), so Buenos Aires is west of the Prime Meridian.

State the latitude as a positive number.

The latitude is

34°\text{S}

, so the positive value is

34°

Answer

(a) Southern hemisphere; (b) West of the Prime Meridian; (c)

34°

Calculating time difference from longitudes

Moderate

Problem

City P is at longitude

30°\text{E}

and City Q is at longitude

105°\text{E}

. Using the rule that

15°

of longitude corresponds to

1

hour of time difference, find the time difference between the two cities. If it is

06{:}00

in City P, what is the local time in City Q?

Find the difference in longitude between the two cities.

\text{Longitude difference} = 105° - 30° = 75°

Divide the longitude difference by 15 to find the time difference in hours.

\text{Time difference} = 75° \div 15 = 5 \text{ hours}

Determine which city is ahead. The city further east has the later local time.

City Q (

105°\text{E}

) is east of City P (

30°\text{E}

), so City Q is

5

hours ahead.

Add the time difference to the time in City P to find the local time in City Q.

06{:}00 + 5\text{ h} = 11{:}00

Answer

The time difference is

5

hours. It is

11{:}00

in City Q.

Local arrival time for a westward flight

Challenging

Problem

A flight departs from City A at longitude

75°\text{E}

10{:}00

local time and flies west to City B at longitude

15°\text{W}

. The flight takes

9

hours. Using

15°

of longitude

= 1

hour, determine the local time in City B when the plane arrives.

Find the longitude difference. Since City A is east and City B is west, add the two longitude values.

\text{Longitude difference} = 75° + 15° = 90°

Calculate the time difference and note the direction.

\text{Time difference} = 90° \div 15 = 6 \text{ hours}

City B is west of City A, so City B is

6

hours behind City A.

Find the arrival time in City A's local time by adding the flight duration to the departure time.

10{:}00 + 9\text{ h} = 19{:}00 \text{ (City A local time)}

Convert to City B's local time by subtracting the time difference (City B is behind).

19{:}00 - 6\text{ h} = 13{:}00

Answer

The plane arrives at

13{:}00

local time in City B.

Practise

Q1·Straightforward

Sydney, Australia, is located at approximately

34°\text{S},\ 151°\text{E}

. Which hemisphere is Sydney in?

Northern hemisphereSouthern hemisphereEastern hemisphereWestern hemisphere

Explanation

The latitude

34°\text{S}

means

34°

south of the equator, so Sydney is in the Southern hemisphere.

Q2·Straightforward

A ship is positioned at

45°\text{N},\ 30°\text{W}

. In which direction from the Prime Meridian is the ship?

NorthSouthEastWest

Explanation

The longitude

30°\text{W}

means

30°

west of the Prime Meridian, so the ship is west of the Prime Meridian.

Q3·Straightforward

A city is located at

34°\text{S},\ 151°\text{E}

. What is the latitude of this city? State your answer as a positive number of degrees.

Explanation

The notation

34°\text{S}

means a latitude of

34°

south of the equator. The latitude is

34°

Q4·Straightforward

The Prime Meridian passes through Greenwich, England, at longitude

0°

. Tokyo is at longitude

140°\text{E}

. How many degrees east of the Prime Meridian is Tokyo?

Explanation

140°\text{E}

means

140°

east of the Prime Meridian, so Tokyo is

140°

east.

Q5·Moderate

City A is at longitude

15°\text{E}

and City B is at longitude

75°\text{E}

. Using the rule that

15°

of longitude equals

1

hour of time difference, calculate the time difference between the two cities in hours.

Explanation

Longitude difference

= 75° - 15° = 60°

. Time difference

= 60 \div 15 = 4

hours.

Q6·Moderate

London is at longitude

0°

and Bangkok is at approximately

105°\text{E}

. Using the rule that

15°

of longitude equals

1

hour of time difference, how many hours ahead of London is Bangkok?

Explanation

Longitude difference

= 105° - 0° = 105°

. Time difference

= 105 \div 15 = 7

hours. Bangkok is east of London, so Bangkok is

7

hours ahead.

Q7·Moderate

City A is at longitude

30°\text{W}

and City B is at longitude

60°\text{E}

. Using the rule that

15°

of longitude equals

1

hour, calculate the time difference between the two cities in hours.

Explanation

The cities are on opposite sides of the Prime Meridian, so the total longitude difference

= 60° + 30° = 90°

. Time difference

= 90 \div 15 = 6

hours.

Q8·Moderate

Using the rule that

15°

of longitude equals

1

hour of time difference, what is the time difference between a city at longitude

120°\text{E}

and a city at longitude

30°\text{W}

6 hours8 hours10 hours12 hours

Explanation

Longitude difference

= 120° + 30° = 150°

(cities on opposite sides of the Prime Meridian). Time difference

= 150 \div 15 = 10

hours.

Q9·Challenging

A city at longitude

105°\text{E}

has local time

12{:}00

. Using the rule that

15°

of longitude equals

1

hour, what is the local time (in

24

-hour format as a whole number of hours) in a city at longitude

45°\text{W}

Explanation

Longitude difference

= 105° + 45° = 150°

. Time difference

= 150 \div 15 = 10

hours. The city at

45°\text{W}

is west, so its local time is

10

hours behind. Local time

= 12{:}00 - 10\text{ h} = 02{:}00

Q10·Challenging

City A is at longitude

75°\text{W}

and City B is at longitude

15°\text{E}

. Using the rule that

15°

of longitude equals

1

hour, calculate how many hours ahead of City A is City B.

Explanation

Longitude difference

= 75° + 15° = 90°

. Time difference

= 90 \div 15 = 6

hours. City B is east, so it is

6

hours ahead of City A. When it is

14{:}00

in City A, it is

14{:}00 + 6 = 20{:}00

in City B.

Q11·Challenging

A plane departs from a city at longitude

60°\text{E}

08{:}00

local time and flies west to a city at longitude

15°\text{W}

. The flight takes

9

hours. Using

15°

of longitude

= 1

hour, what is the local time at the destination when the plane arrives? Give your answer in

24

-hour format as a whole number of hours.

Explanation

Longitude difference

= 60° + 15° = 75°

. Time difference

= 75 \div 15 = 5

hours; the destination is west, so

5

hours behind. Arrival in departure city's time:

08{:}00 + 9\text{ h} = 17{:}00

. Destination local time

= 17{:}00 - 5\text{ h} = 12{:}00

Q12·Challenging

A message is sent from a city at longitude

165°\text{E}

23{:}00

local time. Using

15°

of longitude

= 1

hour, what is the local time (in

24

-hour format as a whole number of hours) in a city at longitude

75°\text{W}

at that moment?

Explanation

Longitude difference

= 165° + 75° = 240°

. Time difference

= 240 \div 15 = 16

hours. The city at

75°\text{W}

is west, so its local time is

16

hours behind.

23{:}00 - 16\text{ h} = 07{:}00