How can I make this into a rational equation?

Question

You have 65 minutes to take an exam of 24
questions. After you finish the first 13 questions,
you realize you must answer the remaining
questions twice as fast to finish the
exam.
How many questions per minute were you
answering?

Answer 1

65 minutes to do 24 questions

after 13, 11 remain

twice a fast means 1/3 of 65 minutes for the last 11 questions

with 2/3 of 65 minutes for the first 13 questions

you did 13 questions in 44 minutes and 20 seconds

you did the last 11 in 21 minutes and 40 seconds, twice as fast

13/44 1/3 questions per minute about a little slower than 1/3 question per minute for 13 questions in about 44 minutes. 1/3 page per minute for 44 minutes = about 13 questions

11/21 2/3 pages per minute or about a little faster than 1/2 question per minute for 11 questions in about 22 minutes. 1/2 page per minute for 22 minutes = 11 questions