Rachel is training for a cycling tournament. She can bike 2 1/4 miles in 1/5 of an hour. At this rate, how many miles can she bike in 1 1/3 hours?

Rachel can bike 2 1/4 miles in 1/5 of an hour, so she can bike 2 1/4 / 1/5 = 9 miles in 1 hour.

So in 1 1/3 hours, she can bike 9 x 4/3 = <<9*4/3=12>>12 miles. Answer: \boxed{12}.