The vertical and horizontal imaginary lines that conform to the spherical shape of the Earth are called the longitudes and the latitudes, respectively. The purpose of these lines are to locate exactly the geographical location of every place on Earth. It's usually applied in aeronautics to aid them during their travels.
Since a sphere has a cross sectional area of a circle, it's revolution has a total of 360°. You should divide this evenly to the 24 existing time zones. Therefore, the angle measurement of the width of longitude for each time zone is 360°/24 = 15°. Each time zone has 15° width of longitude.
For the second question, we use dimensional analysis. This approach is used when you cancel out units that appear both in the numerator and denominator side. The simplified unit should conform to what is asked. In this case, it should be miles per time zone. The solution is as follows:
60 miles/° longitude × 15° longitude/time zone = 900 miles/time zone
Thus, each time zone is approximately 900 miles wide at the equator.