pythagorean formula word problem

[sweetroca888]

Two cars left an intersection at the same time. One traveled west, and the other traveled 14 miles less, but to the south. How far apart were they then, if the distance between them was 16 miles more than the distance traveled south?

 

[arthur ohlsten]

let x = distance traveled to the west
then x-14 is distanced moved to the south
the hypoteneuse = x-14+16

from the right triangle
x^2+[x-14]^2=[x+2]^2 for x greater than 14
x^2+[x^2-28x+196]=x^2+4x+4
x^2-32x+192=0

factors 1 1,1
factors 192 = 1,192 2,96 4,48 6,32 8,24 12,16
we want a set whose sum is 32 8 and 24 does it

[x-8][x-24] =0
x=8 not a solution
x=24 answer

Arthur