Average Rate

Danielsville is 20 miles from 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?

Distance = Rate * Time, i.e. D=RT

Let the time it takes to go from Athens to Danilesville be T1 at a rate R1.
Similarly, let the time it takes to go from Danielsville to Athens be T2 at a rate R2.

Since the distance is the same both ways, D = R1T1 = R2T2
2D = R1T1 + R2T2
2D = R(T1 + T2)
2 = (R/D)(T1 + T2)
2 = R[(T1/D) + (T2/D)]

Since D=RT, R=D/T. Thus, T/D =1/R.
Hence, 2 = R [(1/R1) + (1/R2)]
2 = R [(1/SqRt(1)) + (1/SqRt(2))]
* [(1/R1) + (1/R2)]





Back to Beth's page
Back to Angie's page
Back to Teisha's page