Question 183868
Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

Average speed =(Total Distance)/(Total Time)

Let r=speed of the boat in still water
Distance upstream=(r-5)*(1/2)  {30 min=1/2 hr}
Distance downstream=(r+5)*(5/12)

Distance Upstream = Distance Downstream, so:
(r-5)(1/2)=(r+5)(5/12)  multiply each term by 12
6(r-5)=5(r+5)  get rid of parens
6r-30=5r+25  subtract 5r from and add 30 to each side
6r-5r-30+30=5r-5r+25+30  collect like terms
r=55 mph---------------------speed of the boat in still water
Distance Upstream =(50-5)*(1/2)=25 mi
Distance Downstream=(55+5)*(5/12)=25 mi
Total distance=50 mi
Total Time=(5/12)+(6/12)=11/12 hr
Average Speed of Boat =50/(11/12)=54.5 mph

Hope this helps---ptaylor