Claudia can paint a house 4 times as fast as jan can. The year they worked together it took them 8 days. How long would it take each to paint the house alone ?

Number of days Jan will take to complete painting work alone is 40 days and Claudia will alone take 10 days to paint complete house.Solution:Given that  Claudia can paint a house four times as fast as Jan can.let’s assume house painted by Jan in one day = xSo house painted by Claudia in 1 day = 4xHouse painted by Jan in 8 days = 8 x house painted by Jan in 1 day = 8xHouse painted by Claudia in 8 days = 8 x house painted by Claudia in 1 day = 8 [tex]\times[/tex] 4x = 32xAs painting is completed in 8 days , so complete work of painting = House painted by Jan in 8 days + House painted by Claudia in 8 days = 8x + 32x = 40xSo 40x represent complete work of painting house.Work of painting done by Jan in 1 day = xif Jan alone do the work, number of days required by Jan [tex]=\frac{\text { Complete work }}{\text { work Jan can do in one day }}[/tex][tex]=\frac{40 x}{x}=40 d a y s[/tex]Work of painting done by Claudia in 1 day = 4xIf Claudia alone do the work, number of days required by Claudia [tex]=\frac{\text { Complete work }}{\text { work Claudia can do in one day }}[/tex][tex]=\frac{40 x}{4 x}=10 d a y s[/tex]Hence number of days Jan will take to complete painting work alone is 40 days and Claudia will alone take 10 days to paint complete house.