The uniform distribution is a rectangular shaped distribution. It
is a rectangle that has a base 200-30 = 170 seconds long and an area 
of 1, which represents a probability of 1 that they will wait no less
than 30 seconds nor more than 200 seconds.  

    A = b·h
    1 = 170·h
1/170 = h

Think of it as this rectangle

 ______________________
|______________________|  height = 1/170 units
   base = 170 seconds

The probability that a rider must wait between 1 minute and 1.5 minutes
is just a slice of this rectangle whose base is between 1 minute and
1.5 minutes which is 1.5-1 = .5 minutes or 30 seconds.

Such a slice might look like this:
 __
|__|  height = 1/170 units
base = 30 seconds

The area of this slice would be base·height = 30·(1/170) = .1765

Edwin