+0

Keeps changing his mind

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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. $$\frac{3}{2}$$

Feb 15, 2019

#1
+53
+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.

Feb 15, 2019
#2
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ouch this is good i didnt answer this isnt it!

StarStrike  Feb 15, 2019
#3
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I know its a AMC 10B problem because I also took the AMC 10B

Mathcounts24  Feb 15, 2019
#4
+4568
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the amc10b has passed just to let you know.

tertre  Feb 15, 2019
#5
+53
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ya I figured that out like right after I posted the second message

Mathcounts24  Feb 15, 2019
#6
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what is an amc 10B test? Im just wondering.

ilovepuppies1880  Feb 15, 2019
#7
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I posted that on the AIME post, look at that

Mathcounts24  Feb 18, 2019