Help me understand the (continuous) uniform distribution I think I didn't pay attention to uniform distributions because they're too easy.
So I have this problem

  
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*It takes a professor a random time between 20 and 27 minutes to walk from his home to school every day. If he has a class at 9.00 a.m. and he leaves home at 8.37 a.m., find the probability that he reaches his class on time.
  

I am not sure I know how to do it. I think I would use $F(x)$, and I tried to look up how to figure it out but could only find the answer $F(x)=(x-a)/(b-a)$.
So I input the numbers and got $(23-20)/(27-20)$ which is $3/7$ but I am not sure that is the corret answer, though it seems right to me.
I'm not here for homework help (I am not being graded on this problem or anything), but I do want to understand the concepts. Too often I just learn how to do math and don't "really" understand it. 
So I would like to know how to properly do uniform distribution problems (of continuous variable) and maybe how to find the $F(x)$. I thought it was the integral but I didn't get the same answer.
Remember I want to understand this. Thanks so much for your time. 

Your arrival time is at a constant interva; $[a,b]$ and the uniform distribution gives,
$\int_{a}^{x} \frac{dt}{27-20}$
Your starting point, 8:37, is your time 0 and you want to make it to your class by 9. Your minimum walking time is 20 mins which would give make you still on time. But for a walking time of more than 23 mins you will be late. Hence we want our walking time in $[20,23]$ And these are the bounds of our integral.
Hence desired probability is $3/7$
