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.
How do I write out this equation? I either can't factor the trinomial (such as x^2+3x-6) because it's prime or I get an unrealistic answer like 16 or -6.

Question

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.
How do I write out this equation? I either can't factor the trinomial (such as x^2+3x-6) because it's prime or I get an unrealistic answer like 16 or -6.

kamibug · Answer

We can use fractions. :)
The numerator of 1 represents the room they're painting. 
j represents how long it takes Jeniffer to paint the room. 
j-3 represents how long it takes Carl to paint the room. 
And 2 represents how long it takes them when they work together. 
You need to make common denominators first. 
Once we have common denominators, we can ignore the numerators and solve he denominators as an equation to find j.|dw:1419274083806:dw|