EMT 725
Philippa M. Rhodes
Danielsville is 20 miles frm Jim's home in Athens. He Drives 60 mph going to a meeting (he is almost late) but coming home the weather is bad and drives 30 mph. What is his average speed for the time he is on the road?
Let d = distance, r = rate, and t = time, then we know that
d = r t.
Since there are two times and two distances, let 
and 
be
the rate and time for the the trip to Danielsville, and let 
and 
represent
the rate and time of the return trip.
So, = d / = 20 / 60 = 1/3 hr = 20 minutes, and
= d/ = 20 / 30 = 2/3 hr = 40 minutes.
Thus, the total distance, 
, equals the total time, (+), times the average
rate, 
.
40 = (1/3 + 2/3)
= 40 mph
Generalized Formula,
2 d = (+)
= 2 d / (d/+ d/ )
= 2 / (1/ + 1/)
= (2 ) / (+ )