**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 ) / (+ )