SOLUTION: carmen can weed the garden in 24min. if kim helps they can finish in 8 min. how long would it take kim working alone?

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Question 279072: carmen can weed the garden in 24min. if kim helps they can finish in 8 min. how long would it take kim working alone?
Found 2 solutions by oberobic, scott8148:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
For jobs like this, look at it terms of the whole job being a unitary thing.
Carmen can do the job in 24 minutes, so she does the job at a rate of 1/24 of the total job per minute.
Carmen and Kim working together can do the job in 8 minutes, so their combined rate is 1/8 per minute.
Algebraically, their combined speeds can be shown as:
+1%2F24+%2B+1%2Fx+=+1%2F8+
Multiplying through by 24x we have
x+%2B+24+=+24x%2F8+=+3x
Subtracting x from both sides
24+=+2x
2x+=+24
Dividing both sides by 2
x+=+12
Kim can do the job in 12 minutes working alone.
.
Checking our work, we were told that combined they did the job in 8 minutes.
In 8 minutes, Carmen can do 8%2A%281%2F24%29+=+8%2F24+=+1%2F3 of the job.
In 8 minutes, Kim can do 8%2A%281%2F12%29+=+8%2F12+=+2%2F3 of the job.
1/3 + 2/3 = 1 job.
.
Done

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
in 8 min, Carmen weeds 8/24 or 1/3 of the garden

this means Kim weeds 2/3 of the garden in 8 min ___ so it would take her 12 min [8 / (2/3)] to weed alone