Since they blink at the same rate, the number of blinks per minute must be equal between the two periods of time. Therefore,
85 blinks / 15 minutes = x blinks per minute
51 blinks / y minutes = x blinks per minute
Since the rates are equal, you can set these two proportions equal to each other.
85 blinks / 15 minutes = 51 blinks / y minutes
85 * y = 51 * 15
y = (51 * 15) / 85 = 9 minutes