Apole is standing vertically in a lake in such a way that 1/5 of the pole is in the mud, 2/3 of the pole is in the water, 1/8 of the pole is above the water, and an additional piece of the pole is broken off. the broken piece is 1 foot 3 inches. what is the depth of the lake at the location of the pole?

The first thing we must calculate in this case is the total height of the post, which in this case will be given by:
 1/5 * 100 = 0.2 * 100 = 20%
 2/3 * 100 = 0.6667 * 100 = 66.67%
 1/8 * 100 = 0.125 * 100 = 12.5%
 The broken pierce is 1 foot 3 inches or equivalently 1.25 feets.
 This represents the remaining percentage:
 100-12.5-66.67-20 = 0.83%
 Then, using a rule of three we can get the height of the post
 1.25 ---> 0.83%
 x > 100%
 Clearing x we have_
 x = (100 / 0.83) * (1.25) = 150.60 feets.
 2/3 of the pole is in the water. Therefore, the depth of the lake is
 d = 150.60 * (2/3) = 100.4 feets
 answer
 the depth of the lake at the location of the pole is 100.4 feets