Let's first convert the mixed fraction to an improper fraction.
22/5 km can be written as 4 2/5 km.
To find the speed, we'll divide the distance by time.
Speed = Distance / Time
The distance the motorcyclist traveled is 4 2/5 km, and the time is 2/3 hour.
To add the whole number and fraction, we multiply the fraction by the divisor of the whole number.
Speed = (4 * 5 + 2) / 5 * 3
Speed = (20 + 2) / 15
Speed = 22 / 15
To simplify the fraction, we can't divide both numbers evenly, so we leave it as 22/15 km/h.
Therefore, the motorcyclist was traveling at a speed of 22/15 km/h.
