SOLUTION: Mrs. Jones would take 6 hours less time than her daughter to can all the tomatoes from their garden. Together they could do the job in 1/3 the time it would take the daughter alon

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Question 123636: Mrs. Jones would take 6 hours less time than her daughter to can all the tomatoes from their garden. Together they could do the job in 1/3 the time it would take the daughter alone. How long would Mrs. Jones take to can the tomatoes by herself?
___hrs
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= daughters time in hours. 1/x = part of the job daughter can do in 1 hr.
mother's time = x-6. 1/x-6 = part of the job mother can do in 1 hr.
Job's time = x/3. 3/x = part of the job that can be done in 1 hr.
1/x + 1/x-6 = 3/x LCD=x(x-6)
x-6 + x = 3(x-6)
2x-6=3x-18
2x-2x-6=3x-2x-18+18
x=12
12-6=6 hrs mother's time.
.
Check:
1/12 + 1/6 = 3/12 = 1/4 of the job in 1 hr. Job takes 4 hrs which is 1/3 the time it would take the daughter working alone.
.
Ed