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.