Question 975007
Very little information is given in the description.  The question asks for a rate for the average rate on the trip d to be 50 mph.


RT=D, uniform rates rule for travel.



___________________speed_____________time___________distance
firsthalf__________30_________________(___)__________d/2
secndhalf__________r_________________(____)__________d/2
Totals______________________________(____)___________d


___________________speed_____________time__________________distance
firsthalf__________30________________d/(2*30)_______________d/2
secndhalf__________r_________________d/(2r)_________________d/2
Totals______________________________d(1/(2*30)+1/(2r))___________d



The time and distances sums can form the expression for average rate which must be equated to 50.   {{{distance/time}}}:


{{{highlight_green(d/(d(1/60+1/(2r)))=50)}}}


{{{1/(1/60+1/(2r))=50}}}


{{{1/(r/(60r)+30/(60r))=50}}}


{{{1/((r+30)/60r)=50}}}


{{{60r/(r+30)=50}}}


{{{6r/(r+30)=5}}}


{{{6r=5(r+30)}}}


{{{6r=5r+150}}}


{{{highlight(r=150)}}}, very very fast if in mph.