Efrida and Frazer who live 10 miles apart, meet at a restaur

Question

Efrida and Frazer who live 10 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?

A. 6
B. 7
C. 8
D. 10
E. 11

Show Answer

Official Answer

C

A. 6 
B. 7 
C. 8 
D. 10 
E. 11

Bunuel · Answer

Please check the questions when posting and format them properly. Efrida and Frazer who live 10 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home? A. 6 B. 7 C. 8 D. 10 E. 11 It's a simple geometry problem. Look at the diagram below: Restraunt.PNG From above it follows that the restaurant is 8 miles from Frazer's home and 6 miles from Efrida's home. Answer: C.

chiccufrazer1 · Answer

thanks bunuel..i really appreciate on how you have solved the problem..i also used the same terms except for x +2 which i ended up using x-2 instead..i did use the pythagorean theorem but i ended up getting something like wrong and getting more confused

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Posted from my mobile device

shreerajp99 · Answer

I also did the same thing as frazer and got it wrong.

chiccufrazer1 · Answer

bunuel i have noticed one thing on how your have illustrated the information given in the diagram..the diagram indicates frazer's home as directly west of the restaurant rather than as directly east..does the direction change anything at all?

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Posted from my mobile device

Bunuel · Answer

The stem says that the restaurant is directly east of Frazer's home, hence Frazer's home is directly west of the restaurant. Though it wouldn't change anything even if it were vise-versa.

marcoppe · Answer

Bunuel,

did you apply the pythagorean theorem to the diagram above? I tried to apply it, but I get 6 and -8 as a result.

A second way that I was thinking about is the 90-60-30 degree triangular rule where the sides of the triangle are 3, 4, and 5. However, we are not certain that this triangle has this property.

chiccufrazer1 · Answer

@marcoppe most definitely bunuel used the pythagorean theorem..it is as it is because of the word DIRECTLY NORTH OR DIRECTLY EAST in the stem question signifying that we have a 90 degrees angle somewhere..well marcoppe am sorry awil ask you a dumb question but please bear with me..what does the 90-60-30 triangular rule state?and how do you apply it?

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marcoppe · Answer

@chiccufrazer1

The 90-60-30 rule, sometimes called "Pythagorean triple" or "3-4-5 triangle", applies to those triangles that hold this property: 90°, 60°, and 30° angles. The sides of any 90-60-30 degree triangle will have its sides bearing specific length proportions: 3, 4, 5. There would be no need, therefore, to use the Pythagorean theorem in such cases.

The triangle formed in the excercise above will certainly be a 3-4-5 triangle as we have a 3-4-5 proportion in the length of its sides.

chiccufrazer1 · Answer

@marcoppe. in other words what you trying to say is that we might be given a triangle that only has one side given but holds the 90-60-30 property and can still be able to find the other sides by using the pythagorean triple..if saw then how would test for the 90-60-30 property?

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Bunuel · Answer

90-60-30 (angles) triangle and 3-4-5 (sides) triangle are not the same. For more check here: math-triangles-87197.html

marcoppe · Answer

Thanks Bunuel, I realized now that I got confused with the two principles. To know that we are dealing with a 3-4-5 right triangle there is no need to know its angles.

Sorry chiccufrazer1.

Anyways, I was curious to know how Bunuel got that result. I am pretty sure he used the pythagorean theorem, but I got -8 and 6 using Phythagora. I am not sure how to decide which one to pick.

Bunuel · Answer

Actually I didn't use Pythagorean theorem.

We know that the hypotenuse is 10 and one leg is 2 more than the other, which means that it should be 6-8-10 right triangle.

If we use the theorem then we'll have x^2+(x+2)^2=10^2 --> 2x^2+4x-96=0 --> x^2+2x-48=0 --> (x-6)(x+8)=0 --> x=6 (discard x=-8 since the distance cannot be negative).

Hope it helps.

amgelcer · Answer

Solved using pure math, but took me more than 3 minutes... the draw is reaaly a shortcut.

Thanks Bunuel for this.

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Efrida and Frazer who live 10 miles apart, meet at a restaur

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