Question

A cyclist traveled 9 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel 45 kilometers, the skater had gone 30 kilometers. What's the speed of the skater?

Answer 1

Answer:

18 kmh

Step-by-step explanation:

Given: Speed of cyclist is 9 km/h more than skater´s speed.

           Distance covered at the given time by cyclist is 45 km and by skater is 30 km.

Let´s assume the speed of skater be "x"

∴ Speed of cyclist will be $(x+9) km/h$

Remember; time= $\frac{Distance}{speed}$

We know the time taken by both cyclist and skater are same.

∴ we can form an equation to find the speed of skater.

Time taken by cyclist= time taken by skater

⇒ $\frac{45}{(x+9)} = \frac{30}{x}$

Multiplying both side by $(x+9)\ and\ x$

⇒ $45x= 30\times (x+9)$

Using distributive property of multiplication

⇒$45x= 30x+270$

Subtracting both side by 30x

⇒$15x= 270$

Dividing both side by 15

⇒$x= \frac{270}{15}$

∴$x= 18\ kmh$

Hence, speed of the skater is 18 kmh