"Marcos and Jennifer want to paint over the graffiti on a wall of a building...."

[bubblesxX]

Marcos and Jennifer want to paint over the graffiti on a wall of a building. If Marcos works alone, he can do the job in 20 hours. If Marcos and Jennifer work together, it will take them 12 hours. How long would it take Jennifer to paint the wall working alone?

 

[MarkFL]

Can you show what you've tried and where you're stuck so we know how to best provide help?

 

[Dr.Peterson]

I've seen several ways to carry out the work, but the basic idea is to think in terms of rates: how many jobs per hour can each work, and how many jobs per hour will they do together? One of these will be a variable.

 

[MarkFL]

Marcos and Jennifer want to paint over the graffiti on a wall of a building. If Marcos works alone, he can do the job in 20 hours. If Marcos and Jennifer work together, it will take them 12 hours. How long would it take Jennifer to paint the wall working alone?

I would let \(J\) be the time it would take Jennifer to paint the wall alone. In one hour, Marcos could get 1/20 of the job done alone, and Jennifer would get 1/J of the job done alone, and working together, they would get 1/12 of the job done. This leads to the equation:

[MATH]\frac{1}{20}+\frac{1}{J}=\frac{1}{12}[/MATH]
Can you proceed?

 

[MarkFL]

To follow up:

[MATH]\frac{1}{J}=\frac{1}{12}-\frac{1}{20}=\frac{1}{30}\implies J=30[/MATH]
And so we would conclude that it would take Jennifer 30 hours to paint the wall working alone.