For travel from Washington DC to Baltimore by car, a constant speed of 60 mph was maintained. For the return trip, there was a constant speed \(80\) mph. What was the average speed over the whole two-way trip?
+2668 Because it's the same distance, it is \((60 + 80) \div 2 = \color{brown}\boxed{70} \) mph.
+37157 The time at 60 mph d/60
The time at 80 mph d/80
Time for the whole trip 2d / a where a = average
d/60 + d/80 = 2d/a
a = 2d / ( d/60 + d/80) = 2 / ( 1/60 + 1/80) = 2 / ( 7/240) = 68.57 mph average
+130071 At first blush, we might assume that the avg speed = 70 mph
However, the avg speed will actually be slower
Here's an easy formula to figure average speed when the distances are the same going and returning
Avg speed = 2 (product of the rates) /(sum of the rates) =
2 (60 *80) /( 60 + 80) =
9600 / 140 ≈ 68.57 mph
