## Calculation of distance using lines of latitude

Procedures:

- locate the two places involved
- find the latitude difference between the two places

Note: North-North= subtract

North-South= add

South-North= add

Equator-North= add or subtract

Equator-South= add or subtract

- multiply the latitude difference by 111km

1°=111km( 1° of latitude is approx. 111km on **land**)

Example 1

Calculate the distance between S.Africa(30oS) and Spain(40oN)

Solution:

- i) Lat. diff.=30oS+40N=70o

since 1o=111km

therefore, 111×70=7770km

The distance b/w S.Africa and Spain=7,7770km

## Calculation of Local Time using the lines of longitude

Calculation of Local Time using the lines of longitude:

The calculation of local time using the lines of longitude is a fascinating process that allows us to determine the time difference between two places situated at different longitudes on the Earth’s surface. By following a systematic procedure, we can accurately convert the longitude difference into time, enabling us to adjust the local time accordingly. The step-by-step process is as follows:

1. Locate the Two Places:

Begin by identifying the two places on a map or globe. Locate their respective longitudes, which are measured in degrees east or west from the Prime Meridian (0° longitude) that passes through Greenwich, England.

2. Calculate the Longitude Difference:

Next, determine the difference in longitude between the two places. Subtract the longitude of one place from the longitude of the other. Consider that eastward movement results in a positive longitude difference, while westward movement gives a negative **value**.

3. Convert Longitude Difference to Time:

To convert the longitude difference into time, divide the difference by 15. This step is based on the fact that 15° of longitude corresponds to one hour of time difference. The Earth’s circumference is 360°, and there are 24 hours in a day, so each hour accounts for 360° / 24 hours = 15° of longitude.

4. Adjust Time for Direction of Movement:

Depending on the direction of movement (west or east) between the two places, adjust the time accordingly. If moving westward, subtract the time difference from the starting local time; if moving eastward, add the time difference to the starting local time.

By following these steps, you can accurately calculate the local time at the second place in relation to the first place based on their longitudes and the direction of movement. This procedure is essential for travelers, navigators, and anyone needing to coordinate activities across different time zones. Understanding the relationship between lines of longitude and time allows us to navigate the world with precision and efficiency, fostering global communication and connectivity.

Example:

Let’s calculate the local time difference between Place A (longitude: 90°E) and Place B (longitude: 120°W).

Solution:

**i) Longitude difference = 120°W – 90°E**

To calculate the time difference, we first need to convert the west longitude (120°W) to its equivalent east longitude, which is 360° – 120° = 240°E.

Now, the longitude difference = 240°E – 90°E = 150°E

**ii) Conversion to time:**

To convert the difference in longitude between two locations to time, we utilize the fact that every 15 degrees of longitude corresponds to a one-hour time difference. This conversion allows us to determine how many hours ahead or behind one location is in comparison to the other. The steps for the conversion are as follows:

1. Calculate the Longitude Difference:

Begin by determining the difference in longitude between the two locations. This can be done by subtracting the longitude of one location from the longitude of the other. It’s essential to consider the direction of travel, as traveling eastward results in positive longitude differences, while traveling westward gives negative values.

2. Divide by 15:

Next, divide the longitude difference by 15. Since 15 degrees of longitude correspond to one hour of time difference, this step allows us to find the time difference between the two locations in terms of hours. If the result is positive, it indicates that the second location is ahead in time, and if it’s negative, the second location is behind in time.

3. Determine the Time Difference:

Finally, interpret the result to determine the time difference between the two locations. Each whole number represents one hour of time difference. If there’s a decimal **value**, you can convert it to minutes or adjust it accordingly.

For example:

Let’s say Location A is at longitude 75°W, and Location B is at longitude 100°E. We want to find the time difference between these two locations.

Longitude Difference = (Longitude of B) – (Longitude of A)

Longitude Difference = 100°E – 75°W

Now, we need to convert the longitude difference to degrees west since the starting point is west of the ending point:

Longitude Difference = 100°E + 75°W

Longitude Difference = 175°

Next, we divide the longitude difference by 15:

Time Difference = 175° / 15

Time Difference ≈ 11.67 hours

The result indicates that Location B is approximately 11 hours and 40 minutes ahead of Location A in terms of time.

Time difference = 150°E / 15° per hour = 10 hours

**iii) Adjust time according to direction:**

In this scenario, where Place B is situated to the west of Place A, we use the calculated time difference to adjust the local time at Place B in comparison to Place A’s time. Since we know that every 15 degrees of longitude correspond to one hour of time difference, and Place B is 10 hours (or 150 degrees) west of Place A, we subtract this time difference from Place A’s local time to find Place B’s local time.

Let’s illustrate the time conversion step-by-step:

1. Given Information:

Local time at Place A = 12:00 PM

2. Calculate Time Difference:

As previously determined, the time difference between Place B and Place A is 10 hours.

3. Adjust Local Time at Place B:

Subtract the time difference of 10 hours from Place A’s local time to find Place B’s local time:

Local time at Place B = 12:00 PM – 10 hours

4. Accounting for Time Zones:

Since Place B is west of Place A, we must account for the fact that as we move westward across time zones, we “gain” time. Thus, Place B’s local time will be earlier than Place A’s local time.

5. Final Local Time at Place B:

Local time at Place B = 2:00 AM (of the following day)

The result indicates that the local time at Place B would be 2:00 AM of the following day compared to Place A’s time. Therefore, if it is 12:00 PM at Place A, it would be 2:00 AM of the next day at Place B. This time difference reflects the westward shift, indicating that Place B is ahead of Place A in time.

Examples:

- If town A(long.75°W) is 5.00 pm on Friday, what will be the time and day at town B(long.120°E)?

Solution:

- i) Long. diff.=75°+120°=195°
- ii) conversion to time=
__195__(since 15°=1hr)=13hrs

iii) **adjustment of time according to the direction of movt.=5pm+13hrs(add,since it is due east)=6.00am on Saturday**

In this scenario, we are adjusting the time according to the direction of movement and adding 13 hours since the direction is due east. The starting time is 5:00 PM, and we will calculate the new time after adding 13 hours.

1. Given Information:

Starting time = 5:00 PM

2. Adjustment due to Direction of Movement:

Since the direction of movement is due east, we add the specified number of hours to the starting time. In this case, we add 13 hours.

3. Adding Hours to the Starting Time:

Starting time (5:00 PM) + 13 hours

4. Time Conversion:

As we add the hours, we may need to adjust the day of the week accordingly. If adding the hours exceeds the midnight hour (12:00 AM), we will move to the next day. In this case, since the starting time is in the evening (PM), adding 13 hours will take us into the early morning hours (AM) of the following day.

5. Final Result:

The new time after adding 13 hours to the starting time of 5:00 PM will be 6:00 AM.

Moreover, since the direction of movement is due east and we have moved into the next day, the day of the week also changes. If the starting time was on a Friday at 5:00 PM, adding 13 hours will take us to 6:00 AM on Saturday.

Therefore, the adjusted time is 6:00 AM on Saturday.

Read also:

Geography: Meaning, Scope and Value