SOLUTION: Mark travels due north from home. His wife Kay works due west. They leave for work at the same time. By the time Mark is 10 miles from home, the distance between them is 2 miles mo

Question 1186318: Mark travels due north from home. His wife Kay works due west. They leave for work at the same time. By the time Mark is 10 miles from home, the distance between them is 2 miles more than Kay’s distance from home. How far from home is Kay?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Mark travels due north from home. His wife Kay works due west.
They leave for work at the same time.
By the time Mark is 10 miles from home, the distance between them is 2 miles more than Kay’s distance from home.
How far from home is Kay?
:
let x = K's dist from home
then
(x+2) = M's dist from K at this time
:
Draw this out as a right triangle their home is opposite the hypotenuse
label M's leg 10
label K's leg x
label the hypotenuse (x+2), the dist between M and K
:
Solve this using pythag
10^2 + x^2 = (x+2)^2
100 + x^2 = x^2 + 4x + 4
rearrange
x^2 - x^2 + 4x + 4 = 100
4x = 100 - 4
4x = 96
x = 96/4
x = 24 km is K's dist from home
:
:
:
The dist from M to K then is 24 + 2 = 26 mi
Check on your calc enter = 26

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