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
