A pole is standing vertically in a lake in such a way that one fifth of the pole is in the mud. Two thirds are in the water, one eigth is above the water, and a piece of the top, measuring one foot 3 inches is broken off. What is the depth of the lake?

First find the length of the pole, x, using this equation

x = 1/5x + 2/3x + 1/8x + 1'3".............multiply everything by 120

120x = 24x + 80x + 15x + 120'360"......move all x to the left

x=120'360"......................................convert inches to feet

x=150'

2/3 of the pole is in the water so (2/3)*150' is the depth of the lake

100 feet