This will be an oversimplified question for most of you so please pardon my ignorance in advance.
I practice 16th note exercises in which each rhythm, or 16 bars, is practices 20 times each and there are a total of 24 sections of 16 note rhythms. The metronome is set to 152 beats per minute. I was curious and decided to do the math.
Where is my math wrong below?
(16 x 20) = 320 beats per section (24 x 320) = 7,680 total beats in the 24 sections (7,680 / 152) = 50 <- This is how long the math is telling me it would take to finish all sections at 152 beats per minute.
I finish the exercise in around 24 minutes, not 50. I know the answer is simple and probably relates to my warped notion of beat per minute.
@152 beats per minute
1 [ !!!! !!!! !!!! !!!! ] 16 x 20 times
2 [ !!!! !!!! !!!! !!!! ] 16 x 20 times
3 [ !!!! !!!! !!!! !!!! ] 16 x 20 times
...
24[ !!!! !!!! !!!! !!!! ] 16 x 20 times
Trombonist here.
Assuming each bar is in $\frac{4}{4}$ time, we have $16 \cdot 4 = 64$ quarter note beats per phrase. Each phrase is repeated $20$ times, for a total of $64 \times 20 = 1280$ quarter notes. Now your metronome is set to $152$ BPM (i.e., quarter-note 152), so doing this exercise completely should take $\frac{1280}{152} \approx 8.42$ minutes.
Your mistake is treating each sixteenth note as a beat - unless, of course, your time signature is $\frac{k}{16}$. That requires a difference calculation.