Answer:
The speed of the skater is 15 kilometers per hour.
Step-by-step explanation:
Let x be the rate of the skater.
Then the rate of the cyclist is x+15.
Let t represents time, so we get two equations:
(x+15)t = 12 and xt = 6
Now, solving for t;
and 
As t is the same for the skater and the cyclist, we will equate both the equations now.

Solving for x;

=> 
=> 
=> 
x = 15
Hence, the speed of the skater is 15 kilometers per hour.