Reciprocals of sequential rates are additive when the segment lengths are equal

If we want to add rates that happen in sequence, we can do that by adding their reciprocals. For example, if a car drives 60km at the rate of 60km/h (1h) and then back at the rate of 30km/h (2h), we can derive the car was driving for 3h, but we cannot add the rates themselves.

$$\frac{1h}{60km}+\frac{1h}{30km}=\frac{1h}{60km}+\frac{2h}{60km}=\frac{1h+2h}{60km}=\frac{3h}{60km}$$

This only works if the segment lengths are equal (in this case 60km both ways).