A cyclist traveled to 11 kilometers per hour faster than an in-line skater. In the time it took to travel 18 kilometers the skater had gone 9 kilometers. Find the speed of the skater

The speed of the skater is 11 km/h.

Step-by-step explanation:

Let v represent the speed of the skater. If we use the formula x = vt, where x is the distance, v is the speed, and t is the time:

9 = vt (1)

Since the cyclist traveled to 11 kilometers per hour faster than the skater, the speed of the cyclist is v+11 and time is same for both:

18 = (v+11) t (2)

From the equation 1, t = 9/v

From the equation 2, t = 18 / (v+11)

Since the t's are equal:

→ 9/v = 18 / (v+11)

→ 9 (v+11) = 18v

→ 9v + 99 = 18v

→ 9v = 99

→ v = 11