Afather and his son can clean the house together in 9 hours. when the son works alone, it takes him an hour longer to clean than it takes his dad alone. find how long it takes the son to clean alone.

It will take the son 18.55 hours

Step-by-step explanation:

It takes 9 hours for the father and son to clean the house if they work together. This means that their unit rate of working together will be 1/9

When the son works alone, it takes him an hour longer to clean than it takes his dad alone.

Let x = the time it takes the father to clean the house. This means that it takes the son (x+1) hours to clean the house alone.

The unit rate if working of the son will be 1/+1

The unit rate of working of the father will be 1/x

Since they are working simultaneously, their unit rates are additive. Therefore

1/(x+1) + 1/x = 1/9

(x + x + 1)/x(x+1) = 1/9

(2x+1)/(x^2 + x)= 1/9

18x + 9 = x^2 + x

x^2 + x - 18x-9

x°2 - 17x - 9 = 0

Applying the general formula for quadratic equations,

x = [-b+-√b^2-4ac)]/2a

x =[ - -17 +-√-17^2-4(2×1)]/2×1

x = (17+-18.03)/2

x = (17 + 18.03)/2 or x = (17 - 18.03)/2

x = 17.55 or x = -0.515.

The time cannot be negative so it is 17.55

It takes the father 17.55 hours if he works alone.

It will take the son 17.55 + 1 = 18.55 hours