SOLUTION: Dave and Sandy can paint a room together in 4 hrs. Working alone, Dave can paint the room in 2 hrs less time than Sandy can. Find how long it takes Sandy to paint the room alone.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Dave and Sandy can paint a room together in 4 hrs. Working alone, Dave can paint the room in 2 hrs less time than Sandy can. Find how long it takes Sandy to paint the room alone.      Log On


   

Question 739251: Dave and Sandy can paint a room together in 4 hrs. Working alone, Dave can paint the room in 2 hrs less time than Sandy can. Find how long it takes Sandy to paint the room alone.
Answer by checkley79(3341) About Me  (Show Source):
You can put this solution on YOUR website!
1/X+1/(X+2)=1/4
(X+2+X)/X(X+2)=1/4
(2X+2)/(X^2+2X)=1/4 CROSS MULTIPLY.
X^2+2X=4(2X+2)
X^2+2X=8X+8
X^2+2X-8X-8=0
X^2-6X-8=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
X=(6+-SQRT(-6^2-4*1*-8))/2*1
X=(6+-SQRT(36+32)/2
X=(6+-SQRT68)/2
X=(6+-8.246)/2
X=(6+8.246)/2
X=14.246/2
X=7.123 HOURS FOR DAVE.
7.123+2=9.123 HOURS FOR SANDY.
PROOF:
1/7.123+1/9.123=1/4
(9.123+7.123)/(7.123*9.123)=1/4
16.246/64.96=1/4
1/4=1/4