To determine the distance between the cyclist and the motorist at 10 am, we need to calculate the distance each of them has traveled during that time period.
The time between 8:30 am and 10 am is 1.5 hours.
The cyclist travels at a speed of 12 km/h for 1.5 hours: Distance traveled by the cyclist = Speed × Time = 12 km/h × 1.5 hours = 18 km
The motorist travels at a speed of 59 km/h for 1.5 hours: Distance traveled by the motorist = Speed × Time = 59 km/h × 1.5 hours = 88.5 km
Since they are traveling in opposite directions, the distance between them at 10 am is the sum of the distances they traveled: Distance between the cyclist and the motorist = Distance traveled by the cyclist + Distance traveled by the motorist = 18 km + 88.5 km = 106.5 km
Therefore, at 10 am, the cyclist and the motorist will be approximately 106.5 km apart.