SOLUTION: Dan and Karen who live 10 miles apart meet at a cafe that is directly north of Dan's house and directly east of Karen's house. If the cafe is 2 miles closer to Dan's house than to

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Question 338136: Dan and Karen who live 10 miles apart meet at a cafe that is directly north of Dan's house and directly east of Karen's house. If the cafe is 2 miles closer to Dan's house than to Karen's house, how many miles is the cafe from Karen's house?
(A)6
(B)7
(C)8
(D)9
(E)10

Could please solution to the above problem.
Thanks
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The first thing to do is draw yourself a sketch. You end up with a right triangle with the line from Karen's house to Dan's house being the hypotenuse and the restaurant at the right angle vertex.

Then there are two ways to go about this. You can do it the easy way in your head if you say the hypotenuse is 10 and if the triangle were a 3-4-5 right triangle, the two legs would be 6 and 8. And since 6 and 8 differ by 2, Karen's house is 8 miles from the restaurant.

Or you can do it the hard way.

Let represent the distance from Karen's house to the restaurant. Then the distance from Dan's house to the restaurant is

Then Pythagoras:









You can take it from here. Toss the extraneous negative root.


John

My calculator said it, I believe it, that settles it