You are driving home from school steadily at 95.0 km/h for 130 km. it then begins to rain and you slow to 65.0 km/h. you arrive home after driving 3.33 hours. (a) how far is your hometown from school? (b) what was your average speed?

Very simple,Its all about calculating distance using the formula:
D = V x T
where,
V is the speed or velocity
D is distance
T is the time
In the given problem,there are two parts.
Lets do the calculations for both parts separately:
Part 1) Before the rain
Time = 130/95
         = 1.37 hours  
Time taken after the rain = Total time - time taken before the rain  
                                        = 3.34 hours - 1.37 hours
                                        = 1.97 hours 
Distance covered after the rain = 1.97 hours x 65 km/h
                                                  = 128 km
Hence,
a) The total distance covered =  130 + 128
                                           = 258 km
b) Average speed = Total distance/Total time
                             =  260/3.34
                             = 78 km/h