SOLUTION: Beatrice and javier can paint a room in 5 hours. Working alone, javier can paint the room in 2 hours less time than Beatrice can. Find how long it takes her to paint the room alone

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Beatrice and javier can paint a room in 5 hours. Working alone, javier can paint the room in 2 hours less time than Beatrice can. Find how long it takes her to paint the room alone      Log On


   

Question 109808This question is from textbook
: Beatrice and javier can paint a room in 5 hours. Working alone, javier can paint the room in 2 hours less time than Beatrice can. Find how long it takes her to paint the room alone.
 This question is from textbook

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let b= hours for Beatrice to paint the room. j= hrs for Javier to paint room.
j=b-2
The trick of these problems is to take the reciprocals of the hours to do the job. The reciprocal tells us what fraction of the job can be done in 1 hour.
1/b + 1/j = 1/5
1/b + 1/(b-2)=1/5 Replace j with b-2
5(b-2)+5b=b^2-2b multiply both sides by 5b(b-2) to eliminate fractions.
5b-10+5b=b^2-2b
-b^2+2b+5b+5b-10=0
-b^2+12b-10=0
b^2-12b+10=0 multiply each side by -1.
b=.9 too low to be an answer.
b=11.1 hrs approx Answer.
j=9.1 hrs approx
Check:
1/9.1 + 1/11.1 = 1/5 approx
Ed