claudia can paint a home 4 times as fast as jan the year the

claudia can paint a home 4 times as fast as jan. the year they worked together it took them 8 days. how long can it take each to paint the home alone?

Solution

Let T be the time Claudia takes to paint the home

then 4T will ne the time than=t Jan will take to paint the house ,

now lets say the job is 1 and both worked for 8 days

so 8/T + 4/T8 = 1 , solving the equation for T

we get

8/T + 1/2T = 1 ,

(16+1)/(2T) =1

Hence T = 17/2 days or 8.5 days

so claudia takes 8.5 days and Jan will take 4T which is 8.5*4 = 34 days