Question 722710
normal speed r in miles per hour.  The difference between 5:00am and 5:30am is 1/2 hour.


____________speed________________time____________________distance
normal_______r___________________{{{t=144/r}}}_______________________144
late________r+4__________________{{{t-1/2=144/(r+4)}}}___________________144


The normal time being 1/2 hour more than the late time suggests taking the difference between their expressions.  Both expressions may be shown as expressions using r, the rate.


normal time minus late time equals 1/2 hour,
{{{highlight(144/r-144/(r+4)=1/2)}}}.
Multiply left side and right side by {{{2r(r+4)}}} to clear the fractions.
{{{288(r+4)-288r=r(r+4)}}}
{{{288r+1152-288r=r^2+4r}}}
{{{1152=r^2+4r}}}
{{{highlight(r^2+4r-1152=0)}}}, .



{{{r=(-4+sqrt(16-4*(-1152)))/2=(68-4)/2}}}
=32 miles per hour --- ANSWER.