Every day Tim drives to work One Monday morning with heavy t

Every day Tim drives to work. One Monday morning, with heavy traffic, Tim averaged 30 miles per hour on the way in, and 50 miles per hour on the way home. What was Tim

Solution

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