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Henry decides one morning to do a workout, and he walks 3/4 of the way

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Bunuel
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Henry decides one morning to do a workout, and he walks 3/4 of the way [#permalink] New post   15 May 2019, 04:37
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Henry decides one morning to do a workout, and he walks \(\frac{3}{4}\) 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 \(\frac{3}{4}\) of the way from where he is back toward home. When he reaches that point, he changes his mind again 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. 2/3
B. 1
C. 6/5
D. 5/4
E. 3/2
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GoSatyen
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Re: Henry decides one morning to do a workout, and he walks 3/4 of the way [#permalink] New post   16 May 2019, 03:41
Can anyone explain me the question properly or anyone post the correct way to solve this one.

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nick1816
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Re: Henry decides one morning to do a workout, and he walks 3/4 of the way [#permalink] New post   16 May 2019, 05:42
Henry gets stuck between 2 points that are A and B kms away from his house, therefore A=(1/4)B and (2-B)= 1/4(2-A)
B=4A...(1)

(2-B)= 1/4(2-A)
8-4B= 2-A
8- 16A = 2-A
A=6/15=2/5
B= 4*2/5=8/5
|A-B|=|2/5 - 8/5|=6/5
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Re: Henry decides one morning to do a workout, and he walks 3/4 of the way [#permalink] New post   16 May 2019, 15:13
nick1816 wrote:
Henry gets stuck between 2 points that are A and B kms away from his house, therefore A=(1/4)B and (2-B)= 1/4(2-A)
B=4A...(1)

(2-B)= 1/4(2-A)
8-4B= 2-A
8- 16A = 2-A
A=6/15=2/5
B= 4*2/5=8/5
|A-B|=|2/5 - 8/5|=6/5


How do you know that A=(1/4) B? Can you explain this in detail?
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Re: Henry decides one morning to do a workout, and he walks 3/4 of the way [#permalink] New post   17 May 2019, 01:21
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Henry got stuck between 2 points that are A and B kms away from his house is only possible if the distance between A and B is 3/4th of the distance between Point B and home, and 3/4th of the distance between point A and gym. That's the only way he found himself oscillating between those 2 points.

SPatel1992 wrote:
nick1816 wrote:
Henry gets stuck between 2 points that are A and B kms away from his house, therefore A=(1/4)B and (2-B)= 1/4(2-A)
B=4A...(1)

(2-B)= 1/4(2-A)
8-4B= 2-A
8- 16A = 2-A
A=6/15=2/5
B= 4*2/5=8/5
|A-B|=|2/5 - 8/5|=6/5


How do you know that A=(1/4) B? Can you explain this in detail?
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Re: Henry decides one morning to do a workout, and he walks 3/4 of the way [#permalink] New post   19 May 2019, 07:05
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Would very much appreciate an expert response for this problem !
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Henry decides one morning to do a workout, and he walks 3/4 of the way [#permalink] New post   20 May 2019, 19:05
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Bunuel wrote:
Henry decides one morning to do a workout, and he walks \(\frac{3}{4}\) 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 \(\frac{3}{4}\) of the way from where he is back toward home. When he reaches that point, he changes his mind again 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. 2/3
B. 1
C. 6/5
D. 5/4
E. 3/2




In the diagram above, let H be Henry’s home, G the gym, and A and B the two points that he will be walking back and forth between. So we have HG = 2 and if we let HA = x and BG = y, we have HB = 2 - y, AG = 2 - x and, AB = 2 - x - y. Notice that we need to find AB; thus, we need to find the values of x and y. According to the information given in the problem, we have:

(3/4)(2 - x) = 2 - x - y and (3/4)(2 - y) = 2 - x - y

So (3/4)(2 - x) = (3/4)(2 - y), and thus x = y. Therefore, we can simplify the two equations into:

(3/4)(2 - x) = 2 - x - x

3(2 - x) = 4(2 - 2x)

6 - 3x = 8 - 8x

5x = 2

x = 2/5

Since y = x, y = 2/5. Finally, AB = 2 - x - y = 2 - 2/5 - 2/5 = 10/5 - 4/5 = 6/5.

Answer: C
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Re: Henry decides one morning to do a workout, and he walks 3/4 of the way [#permalink] New post   22 May 2019, 06:44
ScottTargetTestPrep wrote:
Bunuel wrote:
Henry decides one morning to do a workout, and he walks \(\frac{3}{4}\) 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 \(\frac{3}{4}\) of the way from where he is back toward home. When he reaches that point, he changes his mind again 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. 2/3
B. 1
C. 6/5
D. 5/4
E. 3/2




In the diagram above, let H be Henry’s home, G the gym, and A and B the two points that he will be walking back and forth between. So we have HG = 2 and if we let HA = x and BG = y, we have HB = 2 - y, AG = 2 - x and, AB = 2 - x - y. Notice that we need to find AB; thus, we need to find the values of x and y. According to the information given in the problem, we have:

(3/4)(2 - x) = 2 - x - y and (3/4)(2 - y) = 2 - x - y

So (3/4)(2 - x) = (3/4)(2 - y), and thus x = y. Therefore, we can simplify the two equations into:

(3/4)(2 - x) = 2 - x - x

3(2 - x) = 4(2 - 2x)

6 - 3x = 8 - 8x

5x = 2

x = 2/5

Since y = x, y = 2/5. Finally, AB = 2 - x - y = 2 - 2/5 - 2/5 = 10/5 - 4/5 = 6/5.

Answer: C


Thank you for the solution!
It was a bit difficult for me to imagine (3/4)(2 - x) = 2 - x - y :|
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Re: Henry decides one morning to do a workout, and he walks 3/4 of the way [#permalink] New post   27 May 2019, 05:32
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bidskamikaze wrote:
ScottTargetTestPrep wrote:
Bunuel wrote:
Henry decides one morning to do a workout, and he walks \(\frac{3}{4}\) 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 \(\frac{3}{4}\) of the way from where he is back toward home. When he reaches that point, he changes his mind again 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. 2/3
B. 1
C. 6/5
D. 5/4
E. 3/2




In the diagram above, let H be Henry’s home, G the gym, and A and B the two points that he will be walking back and forth between. So we have HG = 2 and if we let HA = x and BG = y, we have HB = 2 - y, AG = 2 - x and, AB = 2 - x - y. Notice that we need to find AB; thus, we need to find the values of x and y. According to the information given in the problem, we have:

(3/4)(2 - x) = 2 - x - y and (3/4)(2 - y) = 2 - x - y

So (3/4)(2 - x) = (3/4)(2 - y), and thus x = y. Therefore, we can simplify the two equations into:

(3/4)(2 - x) = 2 - x - x

3(2 - x) = 4(2 - 2x)

6 - 3x = 8 - 8x

5x = 2

x = 2/5

Since y = x, y = 2/5. Finally, AB = 2 - x - y = 2 - 2/5 - 2/5 = 10/5 - 4/5 = 6/5.

Answer: C


Thank you for the solution!
It was a bit difficult for me to imagine (3/4)(2 - x) = 2 - x - y :|


We know that he walks back and forth between point A and point B (which has a distance of 2 - x - y). The problem also says “he changes his mind again and walks ¾ of the distance from there back toward the gym”. That is, at point A, he walks back to B that is ¾ of the distance from point A to G (which is 2 - x in our diagram). Therefore, we have AB = ¾(AG) or 2 - x - y = (¾)(2 - x).
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Re: Henry decides one morning to do a workout, and he walks 3/4 of the way [#permalink]
27 May 2019, 05:32
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