Question 297556
Juan can paint the neighbor's house four times as fast as Ariel.  The year they worked together it took them 8 days.  How long would it take each to paint the house alone?


Let the amount of days Juan takes to do the job be J


Since Juan works 4 times faster than Ariel, then Ariel's time to do the entire job is 4J


This means that Juan can do {{{1/J}}} of the job in 1 day, and


Ariel can do {{{1/4J}}} of the job in 1 day


Now we get: {{{8/(J) + 8/(4J) = 1}}} since it takes both men 8 days to do the entire job


This gives us: 32 + 8 = 4J --------- Mutiplying by LCD, 4J


40 = 4J


Therefore, J, or Juan's time to do the job is: {{{40/4}}} or {{{highlight_green(10)}}} days, which means that Ariel can do the same job in 10*4 days, or {{{highlight_green(40)}}} days.