Question 157291
Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r
Let d= one-way distance;  Total distance=2d
Time required to drive in=d/30
Time required to drive home=d/50
Total Time=(d/30+d/50)

(1) Average Speed =(total distance)/(total time)=
Ave Speed=2d/(d/30+d/50) =
Ave Speed=2d/((5d+3d)/150)=
Ave Speed=2d/(8d/150)  multiply numerator and denominator by 150/8d:
Ave Speed=(2d*150/8d)/(8d/150*150/8d)=
Ave Speed=300/8=37.5 mi/hr

Now from (1) above, we see that:
 Total Distance=(average Speed)*(Total Time) and we know nothing about the time, so we cannot calculate total distance:
If Total Time=1 hr, then Total Distance=37.5 mi
If Total Time=2 hr, then Total Distance=75 mi
etc., etc


Hope this helps--ptaylor