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# Peter lives 12 miles west of school and Bill lives north of the schoo

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Math Expert
Joined: 02 Sep 2009
Posts: 58402
Peter lives 12 miles west of school and Bill lives north of the schoo  [#permalink]

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16 Mar 2018, 09:17
00:00

Difficulty:

35% (medium)

Question Stats:

66% (02:09) correct 34% (02:17) wrong based on 38 sessions

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Peter lives 12 miles west of school and Bill lives north of the school. Peter finds that the direct distance from his house to Bill's is 6 miles shorter than the distance by way of school. How many miles north of the school does Bill live?

(A) 6

(B) 9

(C) 10

(D) $$6\sqrt{2}$$

(E) None of these

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Re: Peter lives 12 miles west of school and Bill lives north of the schoo  [#permalink]

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16 Mar 2018, 09:31
1
Bunuel wrote:
Peter lives 12 miles west of school and Bill lives north of the school. Peter finds that the direct distance from his house to Bill's is 6 miles shorter than the distance by way of school. How many miles north of the school does Bill live?

(A) 6

(B) 9

(C) 10

(D) $$6\sqrt{2}$$

(E) None of these

Imo B.

The shortest distance between bill and Peter's house is the hypotenuse of a right angle triangle with sides x ( what we want to determine - distance of bills house from school ) and 12.

The hypotenuse is given to be ( x + 12) -6 = x+6

Using Pythagoras theorem on this,

We find-

$$x^2 + 12^2 = (x+6)^2$$

$$x^2 + 144 = x^2 + 12x +36$$

$$144 -36 = 12x$$ ( divide by 12 next to avoid subtraction of big numbers )

x = 9.

Hence B.

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Re: Peter lives 12 miles west of school and Bill lives north of the schoo  [#permalink]

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08 May 2019, 01:39
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Re: Peter lives 12 miles west of school and Bill lives north of the schoo   [#permalink] 08 May 2019, 01:39
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