Two airplanes begin 1000 miles apart and fly along lines tha

Two airplanes begin 1000 miles apart and fly along lines that intersect at a right angle. One plane flies an average of 100 MPH faster than the other. If the planes meet after 2 hours, how fast do the airplanes fly?

Solution

Let s = speed of the slower plane
then
(s+100) = speed of the faster plane
:
The distance to the intersection can we written:
2s for the slower plane; one leg of the right triangle
2(s+100) for the faster which is: (2s + 200); the other leg of the right triangle
;
(2s)^2 + (2s+200)^2 = 1000^2
:
4s^2 + (4s^2 + 800s + 40000) = 1000000
:
8s^2 + 800s + 40000 - 1000000 = 0
:
8s^2 + 800s - 960000 = 0
Simplify divide by 8
s^2 + 100s - 120000 = 0
Factor this to
(s - 300)(s + 400) = 0
Positive solution
s = 300 mph is the slow plane
and
300 + 100 = 400 mph is the fast plane