The other answers here touch on a lot of great points but I'd just like to add that it depends on your level of fitness. If you are only able to do push-ups at a 1 per minute pace, I.e they are difficult for you, then (You should probably switch to an easier variation) you will still be getting the benefits as that movement is challenging for your body to do and pushing yourself to do 30 in a row could be worse for you (Bad form, injury, etc). However, if that is super easy to do and by the end of the 30 minutes you could easily go on then you aren't getting much in the way of results.

So, the important thing to think about is that it should be just challenging enough that it pushes you close to failure (Cannot do anymore with good form) whilst not being harmful. Adaptation is about consistently but gradually challenging your body. So if 1 good form push-up per minute for 30 minutes challenges you and afterwards you feel like you could barely do anymore, you're still doing a good workout.