Inching Along Down the Football Field

  • Inching Along Down the Football Field

    PoW ID: 854

    Problem Print

    footballOne fine fall day, Fred the football player decided to do a little math activity with his favorite sport, so he put his ball down on one of the goal lines of the 100-yard field. He then moved it forward half the distance - that is, 50 yards - toward the other goal line. Next he moved it half the remaining distance, 25 more yards.

    He planned to continue in this manner as long as he could, always advancing the ball half the remaining distance toward the other end. Of course, it should be obvious that sooner or later his moves would be quite small, so small in fact that we could say he was truly "inching along."

    The question is: on which move of the ball would the distance first become less than one inch?


    Extra: What would be the total distance that Fred moved the ball after that move? Give your answer rounded to the nearest 100th of an inch.

    Answer Check

    Show Answer

    The 12th move gives the first less-than-one-inch move. It is 0.87890625 inch.