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John is trying to get from point A to point C, which is 20 miles away

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John is trying to get from point A to point C, which is 20 miles away [#permalink]

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John is trying to get from point A to point C, which is 20 miles away to the northeast; however the direct road from A to C is blocked and John must take a detour. John must travel due north to point B and then drive due east to point C. How many more miles will John travel due to the detour than if he had traveled the direct 20 mile route from A to C?

1) The ratio of the distance going north to the distance going east is 4 to 3

2) The distance traveled north going the direct route is 16
[Reveal] Spoiler: OA

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Re: John is trying to get from point A to point C, which is 20 miles away [#permalink]

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clipea12 wrote:
John is trying to get from point A to point C, which is 20 miles away to the northeast; however the direct road from A to C is blocked and John must take a detour. John must travel due north to point B and then drive due east to point C. How many more miles will John travel due to the detour than if he had traveled the direct 20 mile route from A to C?

1) The ratio of the distance going north to the distance going east is 4 to 3

2) The distance traveled north going the direct route is 16

The information given in the question can be summarized as the following diagram.
Attachment:
1.jpg
1.jpg [ 6.86 KiB | Viewed 2591 times ]


1) The ratio of the distance going north to the distance going east is 4 to 3
Let's say \(AB = 4x\). This makes \(BC = 3x\)
Since we have just one variable, and the three sides link together using the pythagoras theorem, we have

\(AB^2 + BC^2 = AC^2\)

=> \((4x)^2 + (3x)^2 = 20^2\)

From here, we can find a unique value of \(x\). Although it will be a quadratic equation, we will have just one value as the negative value for distance isn't possible. Once we know x, we can find the difference of the two distances. ---> Sufficient

2) The distance traveled north going the direct route is 16
Here, the statement directly gives us a value for one of the sides of a right triangle. Using this and the information from the question stem, we can find the two distances and hence their distance. ---> Sufficient

So, the answer is D.

Hope that helps.
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Re: John is trying to get from point A to point C, which is 20 miles away [#permalink]

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Re: John is trying to get from point A to point C, which is 20 miles away [#permalink]

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New post 16 Mar 2017, 09:26
Question stem requires an asumption. "He travels East to B, then North to C" means his paths in B form a right angle.

I just missed it because i did not assume ABC was right triangle.
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Re: John is trying to get from point A to point C, which is 20 miles away [#permalink]

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New post 16 Mar 2017, 10:36
clipea12 wrote:
John is trying to get from point A to point C, which is 20 miles away to the northeast; however the direct road from A to C is blocked and John must take a detour. John must travel due north to point B and then drive due east to point C. How many more miles will John travel due to the detour than if he had traveled the direct 20 mile route from A to C?

1) The ratio of the distance going north to the distance going east is 4 to 3

2) The distance traveled north going the direct route is 16



Let \(AB = a\) and \(BC = b. a^2 + b^2 = 400\) by Pythagoras' theorem.
We have 2 variables and 1 equation.
Thus we need just 1 more equation, and so D is the most likely correct answer using VA method.

Details are as follows.

1) \(a : b = 4 : 3\)
It means \(3a = 4b\) or \(b = \frac{3}{4}a\)
We have \(a^2 +(\frac{3}{4})^2a = \frac{25}{16}a^2 = 400\) or \(a^2 =16^2\).
Hence \(a = 16\) and \(b = 12\).
Therefore, he detours \(8\) ( \(a + b - 20 = 16 + 12 - 20 = 8\) ) miles.

2) \(a = 16\)
From \(a^2 + b^2 = 400\), we have \(256 + b^2 = 400\) or \(b^2 = 144\).
Hence \(b = 12\)
Therefore, he detours \(8\) ( \(a + b - 20 = 16 + 12 - 20 = 8\) ) miles, which is same as 1).

The answer is D as expected with VA method.
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Re: John is trying to get from point A to point C, which is 20 miles away   [#permalink] 16 Mar 2017, 10:36
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