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?

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.