Areferee was standing on a certain yard line as the 1st quarter ended. he walked 41 3/4 yards to a yard line with the same number as the one he just left. how far was the refree from the nearest goal

Refer to the diagram shown below.

The American football field is 100 yds long, 53 1/3 yards wide, and has 10-yard touchdown zones at each end of the field.

Let x = distance of the referee at the end of the quarter from the nearest goal.
The distance between the same yard lines on either side of the  center line is
100 - 2x

This distance is the 41 3/4 yards that the referee walked. Therefore
100 - 2x = 41.75
-2x = 41.75 - 100 = -58.25
x = 29.125 yd  (or 29 1/8 yd)

The referee was  29 1/8 yards (or 29.125 yards) from the nearest goal.