Question

what time is it in a city located at 45 W longitude when it is 2 Am in a city located at 15 W longitude?

Answer 1

Solution:

As you know, the Earth has 24 time zones, which correspond to 360 degrees of longitude.

Therefore $360{}^{\circ} \leftrightarrow 24$ hour $\rightarrow 1$ hour = $15{}^{\circ}$

The difference in longitude between cities is $45{}^{\circ} - 15{}^{\circ} = 30{}^{\circ}$

Both are located west of Greenwich, respectively, time in a city with a longitude of $45\mathrm{W}$ is less than in a city with a longitude of $15\mathrm{W}$. The difference of 30 degrees corresponds to a difference of 2 hours $(\Delta T)$:

$$\frac{24h}{360{}^{\circ}} = \frac{\Delta T}{30{}^{\circ}}$$ $$\Delta T = \frac{24h \cdot 30{}^{\circ}}{360{}^{\circ}} = \frac{24h}{12} = 2h$$

Accordingly, the local time in the city with a longitude of $45\mathrm{W}$ is $2\mathrm{am} - 2 = 0\mathrm{am} \rightarrow 12:00$ (midnight)

Answer: 12:00 (midnight)

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