SOLUTION: Ann and betty work together and complete a sales report in 4 hr. It would take Betty 6 hr longer, working alone to do the job than it would Ann. How long would it take each of the

Question 200899: Ann and betty work together and complete a sales report in 4 hr. It would take Betty 6 hr longer, working alone to do the job than it would Ann. How long would it take each of them to do the job working alone.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes Ann working alone
Then Ann works at the rate of 1/x of the report per hour
Let (x+6)= amount of time it takes Betty working alone
Then Betty works at the rate of 1/(x+6) of the report per hour
Now we are told that Ann and Betty can do the report working together in 4 hours. So Ann and Betty together works at the rate of 1/4 of the report per hour
So we have:
1/x + 1/(x+6)= 1/4 Multiply each term by 4x(x+6)
4(x+6)+4x=x(x+6) get rid of parens
4x+24+4x=x^2+6x subtract x^2 and also 6x from each side
4x+24+4x-x^2-6x=x^2+6x-x^2-6x collect like terms
-x^2+2x+24=0 multiply each term by -1
x^2-2x-24=0-------------------quadratic in standard form and it can be factored
(x-6)(x+4)=0
x=6 and
x=-4 disregard the negative value for x time in this problem is positive
x=6 hrs----amount of time it takes Ann working alone
x+6=6+6=12 hours amount of time it takes Betty working alone
CK
1/6 + 1/12=1/4
2/12 +1/12=1/4
3/12=1/4
1/4=1/4
Hope this helps---ptaylor
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