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Until 1883 , every city and town in the United States kept its own local time. Today, travelers reset their watches only when the time change equals \(1.0 \mathrm{~h}\). How far, on the average, must you travel in degrees of longitude until your watch must be reset by \(1.0 \mathrm{~h}\) ? (Hint: Earth rotates \(360^{\circ}\) in about 24 h.)

Short Answer

Expert verified
15 degrees of longitude.

Step by step solution

01

Understand the problem

We need to determine how many degrees of longitude one must travel for the local time to change by 1 hour.
02

Identify the known data

The Earth rotates 360 degrees in 24 hours. This means every 24 hours, the Earth completes one full rotation, which is 360 degrees.
03

Calculate the degrees per hour

To find out how many degrees the Earth rotates in one hour, divide the total degrees of rotation by the total hours of rotation: degrees per hour = \( \frac{360^{\text{°}}}{24 \text{ h}} \)
04

Simplify the calculation

Perform the division to get the degrees of rotation per hour: \[\frac{360}{24} = 15^{\text{°}}\text{ per hour} \]
05

Conclude the result

Thus, on average, you must travel 15 degrees of longitude for your watch to reset by 1 hour.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

longitude
Longitude is an important concept when it comes to understanding how our world is divided into time zones.
It represents the geographical coordinate that specifies the east-west position of a point on the Earth's surface.
Longitude is measured in degrees (°), and the prime meridian (0° longitude) runs through Greenwich, England.
It divides the Earth into the Eastern and Western Hemispheres.
As you move east or west from the prime meridian, the longitude increases up to 180°.
This system allows for precise time calculations as the Earth rotates every 24 hours.
Travelers often change their watches based on changes in longitude to reflect the correct local time.
degrees per hour
The Earth rotates 360 degrees in 24 hours, which makes calculating time changes straightforward.
To determine how many degrees the Earth rotates per hour, you simply divide the total degrees by the total hours.
This calculation looks like this: \( \frac{360^{\text{°}}}{24 \text{ h}} = 15^{\text{°}} \text{ per hour} \).
This means that for every hour, the Earth rotates 15 degrees of longitude.
This is why, on average, if you travel 15 degrees east or west, the local time will differ by one hour.
This constant rotation rate is crucial for understanding and calculating time zones.
time calculation
Understanding time zones and calculating time based on longitude are essential skills for travelers and anyone dealing with international schedules.
Using the degrees per hour concept, you know that a 15-degree change in longitude corresponds to a 1-hour difference in local time.
So, if you travel from a location at 0° longitude (Greenwich) to a location at 15° east longitude, the local time advances by one hour.
Similarly, traveling west will set your clock back by one hour for each 15-degree difference in longitude.
This allows us to logically and easily determine the local time when moving across different parts of the Earth.
Accurate time calculation is not only convenient but crucial for coordinating international activities, meetings, and travel plans.

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