Quick Math Word Problem

Question

I am having a brain freeze, I can't figure out a way to solve the following word problem and its leaving me so dumbfounded.

Juan can do a job in 5 hours. Juan and Carmen working together can do the same job in 2 hours. How long would it take for Carmen to do the job by herself?

Please provide a detailed explanation.

Answer 1

Juan does 1/5 of the job in 1 hour

Carmen does 1/x of the job in x number of hours

together they do the job in 2 hours

(1/5)(2)+(1/x)(2)=1 job finished

(2/5)+(2/x)=1

multiply both sides by the LCD of 5x

(2/5)(5x)+(2/x)(5x)=1(5x)

2x+10=5x

10=5x-2x

10=3x

x=10/3

x=3 1/3 hours for Carmen to do the job alone