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;
[tex]t=\frac{12}{x+15}[/tex] and [tex]t=\frac{6}{x}[/tex]
As t is the same for the skater and the cyclist, we will equate both the equations now.
[tex]\frac{12}{x+15}=\frac{6}{x}[/tex]
Solving for x;
[tex]12x=6(x+15)[/tex]
=> [tex]12x=6x+90[/tex]
=> [tex]12x-6x=90[/tex]
=> [tex]6x=90[/tex]
x = 15
Hence, the speed of the skater is 15 kilometers per hour.
