Two airplanes are 1000 miles apart on routes that intersect at right angles. One plane flies 100 miles an hour faster than the other. What are their rates if each reaches the intersection in 2 hours?
+33615 Think of the planes as being at the vertices of a right-angled triangle, where the right-angle is where they intersect.
The initial distances of the two planes from the intersection point are x1 and x2 respectively, They have velocities v1 and v2.
Then the following four equations apply:
v1 = x1/2
v2 = x2/2
v2 = v1 + 100
x12 + x22 = 10002
Solve these simultaneous equations to find the velocities.
