Respuesta :
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 [tex]\times[/tex] 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 [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 = 4x
If 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.
