SOLUTION: Hi, I have been trying to solve the below. I realise quadratic equations are involved but have only managed to get as far as 12[(1/x)+(1/x(x+7)]. Every time I try and get any fu

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Hi, I have been trying to solve the below. I realise quadratic equations are involved but have only managed to get as far as 12[(1/x)+(1/x(x+7)]. Every time I try and get any fu      Log On


   

Question 381486: Hi,
I have been trying to solve the below. I realise quadratic equations are involved but have only managed to get as far as 12[(1/x)+(1/x(x+7)]. Every time I try and get any further I get truely odd results! If you could please help.
Thank you!
Charlotte
Bob takes seven hours longer than Norman to paint a house. If they work together, they can paint the house in 12 hours.
How long would it take each one of them, working alone, to paint the house?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

Lettiing x and (x+7)represent the time it takes Norman and Bob alone to do the job.

Question States:  Per hour the Equalizer

  1/x + 1/(x+7) = 1/12  Multiplying each term by 12x(x+7) so as all denominators= 1

 12(x+7) + 12x = x(x+7)

 12x + 84 + 12x = x^2 + 7x

 x^2 -17x - 84 = 0

factoring

(x-21)(x+4)= 0 

 (x+4) = 0

    x = -4  tossing negative solution out

 (x-21) = 0

    x = 21 hrs, time it takes Norman.  Bob 28hrs  ( 21+7)

CHECKING our Answer

 1/21 + 1/28 =  4/84 + 3/84 = 7/84 = 1/12