A deep mountain valley is separated by two vertical cliffs. One cliff is 600 meters high and the other is 400 meters high. A cable car runs from the foot of each cliff to the top of the other cliff. At what height above the ground do the two cable cars cross? Be sure to draw a diagram.

Answer 1

height h
I assume cables are straight
660 on left, 400 on right
distance x on left, y on right from cross point to cliff on ground
x/h = (x+y)/400
y/h = (x+y)/600

h = 400 x/(x+y)
h = 600 y/(x+y)

so 400 x = 600 y
x = 1.5 y
total distance = 2.5 y
2.5 y/600 = y/h
2.5 h = 600
h = 240