a) Divide the total distance 2pi*r (one circumference) by the total time (23.9 h, expressed in seconds).
b) The radius is r cos L where L = latitude. So the total distance around at latitude L is 2pi*r*cos L. The time taken is the same. So you want r cos L to be 1/4 of r.
The earth has a radius of 6.38 x 106 m and turns on its axis once every 23.9 h. (a) What is the tangential speed (in m/s) of a person living in Ecuador, a country that lies on the equator? (b) At what latitude (i.e., the angle in the figure, in degrees) is the tangential speed 1/4 that of a person living in Ecuador?
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