Question

A father 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.

Answer 1

Answer:

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