SOLUTION: TWO MEN PAINTED A ROOM IN 3 HOURS. HOW LONG WOULD IT TAKE EACH WORKING ALONE TO PAINT THE ROOM IF THE FASTER ONE CAN DO IT IN 2 1/2 HRS. LESS THAN THE OTHER ONE? SO WHAT WOULD T

Question 102668: TWO MEN PAINTED A ROOM IN 3 HOURS. HOW LONG WOULD IT TAKE EACH WORKING ALONE TO PAINT THE ROOM IF THE FASTER ONE CAN DO IT IN 2 1/2 HRS. LESS THAN THE OTHER ONE?
SO WHAT WOULD THE EQUTION BE AND HOW WOULD I SOLVE IT.
Found 2 solutions by ankor@dixie-net.com, scott8148:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the key to work problems is finding what portion of the whole job each worker completes

Example: A takes 6 hr and B takes 8 hr, how long together?
in 1 hour; A does 1/6 and B does 1/8 and they complete 7/24 of the job
in x hours; A does x/6 and B does x/8 and they complete 1/1 or the whole job
(x/6)+(x/8)=1 ... 4x+3x=24 ... 7x=24 ... x=24/7 (note relationship to 1 hour's work)

in your problem, you know the time together and you want the individual times ... x and x+2.5

(3/x)+(3/(x+2.5))=1 ... 3(x+2.5)+3(x)=(x)(x+2.5) ... 3x+7.5+3x=x^2+2.5x ... x^2-3.5x-7.5=0

2x^2-7x-15=0 ... (2x+3)(x-5)=0 ... x=-3/2 and x=5 ... negative value not realistic

the times are 5 hr and 7.5 hr

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