Question 907866
Two cars start at the same place and travel at right angles to each other.
 one car travels 2mph faster than the other car
 after 2 hours they are 20 miles apart. 
how fast are the cars traveling?
:
let s = speed of the slower car
then
(s+2) = speed of the faster car
therefore:
2s = distance traveled by the slower car
and
2(s+2) = distance traveled by the faster car
:
We can solve this as right triangle: a^2 + b^2 = c^2, where
a = 2s
b = 2(s+2)
c = 20
{{{(2s)^2 + (2(s+2))^2 = 20^2}}}
{{{4s^2 + (2s+4)^2 = 400}}}
{{{4s^2 + 4s^2 + 16s + 16 = 400}}}
{{{8s^2 + 16s + 16 - 400 = 0}}}
{{{8s^2 + 16s - 384 = 0}}}
simplify, divide by 8
{{{s^2 + 2x - 48 = 0}}}
Factors to 
(s+8)(s-6) = 0
The positive solution is all we want here
s = 6 mph is the speed of the slower car
:
you can find the speed of the faster car, check the solutions in original equation