Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio E of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?  Select the correct option:
A) 8 : 3  B) 3 : 2  C) 4 : 3  D) 2 : 3  E) 3 : 8

Rationale: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio e of ann ' s time to bob ' s time is 3 : 2 . answer : b ."
Answer: B