Explanation: To understand the time difference between Mumbai and New York, we need to consider the longitudinal positions of both cities and their respective time zones.
Mumbai is located at 73 degrees East longitude and follows Indian Standard Time (IST), which is GMT+5:30. New York is located at 74 degrees West longitude and follows Eastern Standard Time (EST), which is GMT-5.
The Earth is divided into 24 time zones, each spanning 15 degrees of longitude. This means that for every 15 degrees of longitude, the time difference is 1 hour. Therefore, the longitudinal difference between Mumbai and New York is 147 degrees (73 degrees East to 74 degrees West).
To calculate the time difference, we divide the longitudinal difference by 15 degrees per hour:
\[ \text{Time Difference} = \frac{147 \text{ degrees}}{15 \text{ degrees/hour}} = 9.8 \text{ hours} \]
However, we must also account for the half-hour difference in IST. Therefore, the total time difference is:
\[ 9.8 \text{ hours} + 5.5 \text{ hours} = 15.3 \text{ hours} \]
Since New York is west of Mumbai, we subtract this time difference from the time in Mumbai to get the time in New York:
\[ 10:00 \text{ am} - 15.3 \text{ hours} = 12:12 \text{ am} \]
Thus, when it is 10 am in Mumbai, it is 12:12 am in New York. This calculation takes into account the longitudinal difference and the specific time zones of both cities, ensuring the correct time difference is applied.
Understanding time zones and their differences is crucial for international travel, communication, and coordination. The concept of time zones is based on the Earth's rotation and the division of the globe into 24 equal parts, each representing an hour of the day. This system allows for a standardized way of measuring time across different regions of the world, facilitating global communication and coordination.