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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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:

Multiplying through by 24x we have

Subtracting x from both sides


Dividing both sides by 2

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 of the job.
In 8 minutes, Kim can do of the job.
1/3 + 2/3 = 1 job.
.
Done

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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