Need the equation for the following problem

Question

man falls down a well of 50 feet.  He climbs up 5 feet each day and slides back 3 feet each night.  How many days does it take home to get out of the well?  I can figure out the answer doing each day, but I am looking for the equation that will give me the answer.

Answer 1

Let x = number of days that it takes to climb out

 

His original position is 50 ft below the ground.  Let's call his original position -50.  During a given 24 hour period, he moves two feet closer to ground level.  So, in x 24 hour periods, he moves upward 2x ft.  When he reaches the ground, he is 50 feet above his initial position.  In relation to ground level, his position is 0.

 

He reaches ground level when -50 + 2x = 0

 

                                                   2x = 50

 

                                                    x = 25 days