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

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Manager
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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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12 Sep 2014, 21:35
4
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45% (medium)

Question Stats:

68% (01:23) correct 32% (01:24) wrong based on 284 sessions

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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

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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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13 Sep 2014, 06:50
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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 [ 6.86 KiB | Viewed 3221 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

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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16 Mar 2017, 10:26
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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16 Mar 2017, 11:36
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]

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07 Jun 2018, 03:21
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Re: John is trying to get from point A to point C, which is 20 miles away &nbs [#permalink] 07 Jun 2018, 03:21
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