Mr. boll can pick a bale of cotton by hand in five days. if his son john joins him in the work they can pick a bale in three days. how long would the son take to do the job?

7 1/2 days.

Days needed to complete full job: Mr. Boll = 5 days Son = x days Together = 3 days 
Amount of job completed per day: Mr. Boll = 1/5 of bale Son = 1/x of bale Together = 1/3 of bale 
Equation: 1/5 + 1/x = 1/3 1/x = 5/15 - 3/15 1/x = 2/15 1 = (2/15)x x = 15/2 <=> 

1/2 days (15/2) 

Days needed to complete full job: 
Mr. Boll = 5 days 
Son = x days 
Together = 3 days 

Amount of job completed per day: 
Mr. Boll = 1/5 of bale 
Son = 1/x of bale 
Together = 1/3 of bale 

Equation: 
1/5 + 1/x = 1/3 
1/x = 5/15 - 3/15 
1/x = 2/15 
1 = (2/15)x 
x = 15/2 

This is just like trying to find the x just have to figure the part out hope this help