Calculating the Difference in Longitude

The question asks us to find the difference in longitude between two places, C and D, given their longitudes.

The given longitudes are:

• Longitude of C = 46° W
• Longitude of D = 64° W

Both places are located in the Western Hemisphere, as indicated by the 'W' (West) designation. When two places are in the same hemisphere (both West or both East), the difference in longitude is found by subtracting the smaller longitude value from the larger longitude value.

Here, the larger longitude value is 64° W, and the smaller value is 46° W.

The calculation for the difference in longitude is:

\(\text{Difference in Longitude} = | \text{Longitude of D} - \text{Longitude of C} |\)

\(\text{Difference in Longitude} = | 64^\circ \text{ W} - 46^\circ \text{ W} |\)

\(\text{Difference in Longitude} = | (64 - 46)^\circ |\)

\(\text{Difference in Longitude} = | 18^\circ |\)

\(\text{Difference in Longitude} = 18^\circ\)

The difference in longitude between place C (46° W) and place D (64° W) is 18°.

Steps to Calculate Longitude Difference (Same Hemisphere)

1. Identify the longitudes of the two places.
2. Check if both longitudes are in the same hemisphere (both East or both West).
3. If they are in the same hemisphere, subtract the smaller longitude value from the larger one.
4. The result is the difference in longitude.

Let's summarize the given information and the result in a table:

Since both are West, the difference is \(64^\circ - 46^\circ = 18^\circ\).

Revision Table: Longitude Concepts

Additional Information: Longitude Difference Calculation

Understanding how to calculate the difference in longitude is fundamental in geography and navigation. The method depends on whether the two places are in the same hemisphere or different hemispheres.

• Same Hemisphere (Both East or Both West): Subtract the smaller longitude from the larger one. Example: 30° E and 50° E have a difference of \(50^\circ - 30^\circ = 20^\circ\).
• Different Hemispheres (One East, One West): Add the two longitude values. Example: 30° E and 50° W have a difference of \(30^\circ + 50^\circ = 80^\circ\).
• Crossing the 180° Meridian: If the sum of longitudes from different hemispheres exceeds 180°, subtract the sum from 360°. This scenario is less common in basic problems but important for full understanding. Example: 150° E and 170° W. Sum = \(150^\circ + 170^\circ = 320^\circ\). Difference = \(360^\circ - 320^\circ = 40^\circ\).

In this specific problem, both locations are in the Western Hemisphere, making the simple subtraction method applicable.