To determine the local time in Nigeria (longitude 15°) when it is 10 PM in Ethiopia (longitude 45°), we need to consider the time difference based on their longitudes.
The Earth is divided into 360 degrees of longitude, and it takes 24 hours for the Earth to complete a full rotation. This means that each degree of longitude corresponds to 4 minutes of time (360 degrees / 24 hours = 15 degrees per hour).
Now, let's calculate the time difference based on the longitudes:
- Longitude of Ethiopia: 45°
- Longitude of Nigeria: 15°
The difference in longitude between Ethiopia and Nigeria is:
\[ 45° - 15° = 30° \]
Next, we convert this angular difference into time:
Since each degree corresponds to 4 minutes, we calculate the time difference:
\[ 30° \times 4 \text{ minutes/degree} = 120 \text{ minutes} \]
120 minutes is equivalent to 2 hours.
Now, since Ethiopia is to the east of Nigeria, we subtract the 2 hours from the local time in Ethiopia to find the local time in Nigeria:
Ethiopia's local time: 10 PM
Subtract 2 hours:
10 PM - 2 hours = 8 PM
Thus, when it is 10 PM in Ethiopia, it will be 8 PM in Nigeria.
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