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 [tex](x+9) km/h[/tex]
Remember; time= [tex]\frac{Distance}{speed}[/tex]
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
⇒ [tex]\frac{45}{(x+9)} = \frac{30}{x}[/tex]
Multiplying both side by [tex](x+9)\ and\ x[/tex]
⇒ [tex]45x= 30\times (x+9)[/tex]
Using distributive property of multiplication
⇒[tex]45x= 30x+270[/tex]
Subtracting both side by 30x
⇒[tex]15x= 270[/tex]
Dividing both side by 15
⇒[tex]x= \frac{270}{15}[/tex]
∴[tex]x= 18\ kmh[/tex]
Hence, speed of the skater is 18 kmh
