Captchar wrote: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?
Refer to the figure above.
C is the Cafe, D is Dan's house and K is Karen's house.
Hence, the hypotenuse, KD = 10
And if KC = x, CD = (x - 2)
So, x² + (x - 2)² = 10² = 100
--> x² + x² - 4x + 4 = 100
--> 2x² - 4x - 96 = 0
--> x² - 2x - 48 = 0
--> x² - 8x + 6x - 48 = 0
--> (x + 6)(x - 8) = 0
Hence, either x = -6 or x = 8
As x cannot be negative, x = 8
The correct answer is C.
