Henry decides one morning to do a workout and walks \(\frac{3}{4}\) of the way from his home to his gym. The gym \(2\) kilometers away from Henry's home. At that point, he changes his mind and walks \(\frac{3}{4}\) of the distance from there back toward the gym. If Henry keeps changing his mind when he has walked \(\frac{3}{4}\)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 \(|A-B|\) ?

A. \(\frac{2}{3}\)

B. \(1\)

C. \(\frac{6}{5}\)

D. \(\frac{5}{4}\)

E. \(\frac{3}{2}\)

CalculatorUser Feb 15, 2019

#1**+1 **

This is an AMC 10B problem. You probably shouldn't post it until everyone has taken the test (maybe next week?). By the way, I was also stuck on this problem.

Mathcounts24 Feb 15, 2019