Alicia can paint a small room 21 hours faster than Nina aloneness 4 hours slower than Alicia and Nina together. How long will it take them to paint the room together

Alicia and Nina together will take 10 hours to paint the room together

Step-by-step explanation:

Let Alicia can paint a house in x hours; that is in 1 hour she can paint 1/xth of the house.

Nina can paint the same house in y hours. Which means in 1 hour she can paint 1/yth of the house.

Since Alicia is 21 hours faster than Nina,

y-x=21

y=x+21

Together in 1 hour they can paint: - 1/x + 1/y = 21+2x/x (21+x)

of the house.

Total Hours for painting the house together will be x (21+x) / 21+2x

Total hours of painting by both is less than 4 hours that of Alicia alone,

21+x (x) / 21+2x=x-4

21x+x^2 = 21x-84+2x^2-8x

x^2-8x-84=0

Solving the quadratic equation

x=14

x=-6

Hence taking the positive value x = 14

Total Hours for painting the house together will be x-4 hours

= 10 hours