Yes. As others said there are too many things uncertain. If I understood what you meant.
data have;
infile cards truncover expandtabs;
input date :date. meal :$10. start :time. stop :time. value;
format date yymmdd10. start stop tod8.;
cards;
02-Jun-25 Sick 16:00:00 16:45:00 465
02-Jun-25 Meal 16:45:00 17:15:00 30
;
data gt30m le30m;
set have;
if intck('minutes',start,stop)>30 then output gt30m;
else output le30m;
run;
data temp_gt30m;
set gt30m;
mystart=start;
do i=start to stop;
if i-mystart=1800 or i=stop then do;myend=i;output;mystart=i; end;
end;
drop i;
format mystart myend tod8.;
run;
data temp_le30m;
set le30m;
mystart=start; interval=(stop-start)/2;
do i=start to stop;
if i-mystart=interval or i=stop then do;myend=i;output;mystart=i; end;
end;
drop interval i;
format mystart myend tod8.;
run;
data want;
set temp_:;
run;