MathDB

Henry decides one morning to do a workout, and he walks

\tfrac{3}{4}

of the way from his home to his gym. The gym is

2

kilometers away from Henry's home. At that point, he changes his mind and walks

\tfrac{3}{4}

of the way from where he is back toward home. When he reaches that point, he changes his mind again and walks

\tfrac{3}{4}

of the distance from there back toward the gym. If Henry keeps changing his mind when he has walked

\tfrac{3}{4}

of the distance toward either the gym or home from the point where he last changed his mind, he will get very close to walking back and forth between a point

A

kilometers from home and a point

B

kilometers from home. What is

|A-B|

<span class='latex-bold'>(A) </span> \frac{2}{3} \qquad <span class='latex-bold'>(B) </span> 1 \qquad <span class='latex-bold'>(C) </span> 1\frac{1}{5} \qquad <span class='latex-bold'>(D) </span> 1\frac{1}{4} \qquad <span class='latex-bold'>(E) </span> 1\frac{1}{2}

18

Problems(2)