SOLUTION: Rob takes 5 hours longer than Jen to paint a room. If they work together, they can paint a room in 6 hours. How long does it take Rob to paint a room by himself?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Rob takes 5 hours longer than Jen to paint a room. If they work together, they can paint a room in 6 hours. How long does it take Rob to paint a room by himself?      Log On


   

Question 435757: Rob takes 5 hours longer than Jen to paint a room. If they work together, they can paint a room in 6 hours. How long does it take Rob to paint a room by himself?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Rob takes 5 hours longer than Jen to paint a room.

Let x and (x+5) represent Jen and Rob's times solo

Question states*** Per hour the Equalizer

 1/x + 1/(x+5) = 1/6   |multiplying thru by 6x(x+5) so as alll denominaotrs=1

 6(x+5) + 6x = x^2 + 5

  x^2 -7x-30 = 0

factoring

(x+3)(x-10)= 0

(x+3)= 0  |Tossing out negative solution for time

(x-10)= 0   x = 10hr, jen's time.  Rob's time is 15hr.   (10hr + 5hr)



CHECKING our Answer***

  1/10 + 1/15 =  3/30 + 2/30 = 5/30 = 1/6