If samantha and logan can do their paper route together in 45 minutes, how many hours would it take each of them to do it alone, given that samantha is three times as fast as logan? what are both of there rates, times and work done?

Here is how I would set up this problem:
Logan: x
Samantha: 3x
Total: 45

Therefore we get the equation:
3x+x=45

Solve this equation for x:
3x+x=45
4x=45
x=11.25

Now refer back to how you set up the problem:
Logan: x
Samantha: 3x
Therefore, Logan's time was 11.25 minutes. To find Samantha's time, do 11.25(3)=33.75 because Samantha is 3 times as fast as Logan.

Logan's time: 11.25 minutes
Samantha's time: 33.75 minutes

To find the rates, you must have a unit of distance because: distance=rate(time)
rate=distance/time

Best of luck!