Question

A referee 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

Answer 1

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)

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