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 miles per hour faster tha the other. if the two planes meet after two hours, how fast do the airplanes fly?

Solution

The speeds can be set up as vectors, which makes them a right triangle the same as the flight paths.
They cover 1000 miles in 2 hours, --> 500 mph total. 500 is the hypotenuse.
The 2 legs differ by 100 mph.
a^2 + b^2 = c^2
a^2 + (a+100)^2 = 500^2
This is the 3, 4, 5 triangle, so the speeds are 300 mph and 400 mph.