Like everyone else in here I’m going to speculate but it would seem to me that throughout the day would be better, as long as each time you are going until muscle failure.
Due to the fact that no matter how good of shape you are in, your form will suffer the more fatigued your muscles are. So if you hit muscle failure after 30 or 40 you should take a break because it doesn’t do you any good to crank out 100 pushups if 60 are in poor form.
Latest Answers