A car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 38 miles per hour, how many hours long is the trip?
Choose the correct answer:  A) 13  B) 14  C) 15  D) 16  E) 17

Rationale: "let t be the total time of the trip . 30 * 5 + 42 ( t - 5 ) = 38 t 4 t = 210 - 150 t = 15 the answer is c ."
Answer: C