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
