The target frequency (F4) is approximately 349.23Hz.
You have to find a common divisor between those two frequencies, which coincidentally is the bar.
So, assuming the frequency above, you can find that each bar happens at
frequency/4. Then, you can find the frequency for the beat by multiplying it by 3 (since the meter is 3/4 - aka, 3 beats per bar), and finally get the actual BPM by multiplying by 60:
F4 = 349.23
barsPerSecond = F4 / 4
beatsPerSecond = barsPerSecond * 3
beatsPerMinute = beatsPerSecond * 60
Consider that the answer from Aaron is perfectly right, but it is based on the ratio of an interval that uses the frequency of the second note as reference. Since you might not know the precision of that reference, it's up to you to decide if you should use the known ratio of the interval (not knowing the tuning it's based on), or the rhythm ratio shown in the example.