In order to determine the rate, calculate the quotient in between 1/3 cups of flour and 1/2 minutes:
(1/3)/(1/2)
take into account that a division between fractions can be written as a multiplication by inverting the second fraction, that is:
(1/3) / (1/2) = (1/3)(2/1) = 2/3
Hence, the rate is:
2/3