Let the radius of the earth be 3560 miles. Suppose you are running westwards along the equator.
How fast would you have to run so that there are 36 hours between the time the sun rises and the time you see it set?
Remember that the earth is rotating beneath you!
Two possible solutions:
If the speed of the earth's rotation is V MPH from west to east, then you could run at a speed that makes your net velocity = 1/3 V from west to east. This would cause the sun to rise in the east and set 36 hours later in the west. So you speed would be V - 1/3V = 2/3V toward the west. Or, you could run twice that speed, or 4/3V; this way your net velocity is -1/3V, and the sun would rise in the west and set in the east.
The value for V is R , or 3560 miles x 2 /24 hours, or 932 MPH. so running at either 621 MPH or 1243 MPH would do the trick.