Carl can paint a room 3 hours faster than jennifer can. if they work together, they can complete the job in 2 hours. using complete sentences, explain each step in figuring out how to determine the time it would take jennifer to complete this job on her own. (10 points)

To solve this question, we should convert the information we have to a system of equation. 
Let x=speed of Carl's painting, in jobs/hour
Let y=speed of Jen's painting, in jobs/hour
We know from the first sentence:
x=3y
Together, they can complete a whole job in 2 hours, which means they complete half a job in 1 hour when they work together
Therefore:
x+y=1/2, meaning Jenn and Carl working together completes half a job/hour
We can substitute 3y for x in this equation to find Jen's rate:
3y + y = 1/2
4y=1/2               Divide both sides by 4
y=1/8

Jenn completes 1/8 of the job in 1 hour, so it would take her 8 hours to do the job herself.

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