Carcass wrote:

Jonna and Russell meet at a diner that is directly south of Jonna's house and directly west of Russell's house. If the diner is exactly 10 miles from Jonna's house and Russell's house is 2 miles closer to the diner than to Jonna's house, how far apart is Russell's house from the diner?

A. 8

B. 14

C. 16

D. 24

E. 26

Here we can draw the diagram as below from the facts given in the statement.

Let the distance between Jonna's house and Russel's house = X

SO the distance between Russel's house and diner = X - 2

By using Pythagoras theorem we have,

\(X^2 = (X - 2)^2 + 10^2\)

or \(4X = 104\)

or \(X = 26\).

Therefore the distance between Russel's house and diner = \(X - 2 = 26 - 2 = 24\)

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