The speed of the first motorcyclist is 65 km/h, and the speed of the second motorcyclist is 58 km/h.
Let's denote the speed of the slower motorcyclist as x km/h. Since the speed of the other motorcyclist is 7 km/h more, the speed of the faster motorcyclist is x+7 km/h.
When two objects are moving towards each other, their relative speed is the sum of their individual speeds. Therefore, the relative speed of the two motorcyclists is x+(x+7)=2x+7 km/h.
After 2 hours, the distance covered by the two motorcyclists is the product of their relative speed and the time they traveled, which is 2(2x+7) km.
The distance between them after 2 hours is given as 34 km. So, we can set up the equation 2(2x+7)=34 and solve for
4x+14=34
4x=20
x=5
Now that we know x, the speed of the slower motorcyclist is 5 km/h, and the speed of the faster motorcyclist is 5+7=12 km/h.
Therefore, the speed of the first motorcyclist is 12 km/h, and the speed of the second motorcyclist is 5 km/h.