An experienced roofer can work twice as fast as her . working together, they can shingle a new section of roof in 4 hours. how long would it take the experienced roofer, working alone, to complete the same job?

For this case, the first thing we must do is define variables.
 We have then:
 x: amount of time the assistant works
 Y: amount of time the experienced person works
 We then have the following system of equations:
 x + y = 4
 y = (1/2) x
 Solving the system we have:
 x = 8/3
 y = 4/3
 
 It would take the roofer, working alone, to complete the same job about:
 y = 4/3 hours