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 = x

So house painted by Claudia in 1 day = 4x

House painted by Jan in 8 days = 8 x house painted by Jan in 1 day = 8x

House painted by Claudia in 8 days = 8 x house painted by Claudia in 1 day = 8 4x = 32x

As 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 = 40x

So 40x represent complete work of painting house.

Work of painting done by Jan in 1 day = x

if Jan alone do the work, number of days required by Jan

Work of painting done by Claudia in 1 day = 4x

If Claudia alone do the work, number of days required by Claudia

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.