Question

bette drives at 60 mph for 2 and a half hours and 75 mph for 1 and a half hours. What is her average rate of speed?

Answer 1

There are a couple of ways to think about this.

1) Weight the speed by the time and compute the weighted average.
   (60*2.5 + 75*1.5)/(2.5 + 1.5) = 65.625
Her average rate of speed is 65.625 mph.


2) Consider distance and time.
   distance = speed * time
   distance₁ = speed₁ * time₁
   distance₂ = speed₂ * time₂
   total distance = distance₁ + distance₂
   total time = time₁ + time₂
And the average speed is given by
   average speed = (total distance)/(total time)

Using the above formulas, we have
   distance₁ = 60 mi/h * 2.5 h = 150 mi
   distance₂ = 75 mi/h * 1.5 h = 112.5 mi
   total distance = 150 mi + 112.5 mi = 262.5 mi

   total time = 2.5 h + 1.5 h = 4.0 h

   average speed = (262.5 mi) / (4.0 h) = 65.625 mi/h


Bette's average rate of speed is 65.625 mph.