+2862 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. \(\frac{3}{2}\)
+53 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.
