Question

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 ?

Answer 1

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 $\times$ 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 $=\frac{\text { Complete work }}{\text { work Jan can do in one day }}$

$=\frac{40 x}{x}=40 d a y s$

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

If Claudia alone do the work, number of days required by Claudia $=\frac{\text { Complete work }}{\text { work Claudia can do in one day }}$

$=\frac{40 x}{4 x}=10 d a y s$

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.