A radio signal transmitted live from Station X, located at longitude 78^\circ\text{E}, is … — JAMB UTME

A radio signal transmitted live from Station X, located at longitude $78^\circ\text{E}$ , is logged at $10:40\text{ AM}$ local solar time. At the exact same instant, the signal is received at Station Y, where the local solar time is logged as $03:16\text{ PM}$ on the same day. What is the longitude of Station Y in degrees East?

Answer: 147 °E

Answer

147°E

The time difference between 10:40 AM and 03:16 PM is 4 hours and 36 minutes. Converting this time difference to degrees using

15^\circ

per hour (

4 \times 15^\circ = 60^\circ

) and

1^\circ

per 4 minutes (

36 \text{ min} / 4 \text{ min/degree} = 9^\circ

) gives a total longitudinal distance of

69^\circ

. Because Station Y has a later solar time than Station X, it is situated further East. Adding

69^\circ

78^\circ\text{E}

yields

147^\circ\text{E}

Step-by-Step Solution

Calculate the time difference between Station Y and Station X

4 hours and 36 minutes

Subtracting the earlier local time at Station X (10:40 AM) from the later local time at Station Y (03:16 PM) yields a duration of 4 hours and 36 minutes.

Convert the calculated time difference into longitudinal degrees

69 degrees

Earth rotates through 15° of longitude per hour (or 1° every 4 minutes). Thus, 4 hours corresponds to 60° and 36 minutes corresponds to 9°, giving a total of 69°.

Calculate the longitude of Station Y based on directional time relationship

147°E

Because local time at Station Y is later than at Station X, Station Y lies further East. Adding the angular separation of 69° to 78°E results in 147°E.

Key Concept

Longitude calculation from local time difference

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