Question

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

Answer 1

The formula for speed is

speed = distance ÷ time.

`s=(d)/(t)`

the cyclist's speed is equal to the in-line skater's speed plus 11 kph, or

`S_c=S_s+11`

Where, Sc is the cyclist's speed and Ss the in-line skater's speed

We also know that, the time it took the cyclist to travel 18 km is the same for the skater to travel 9 km. From the formula for speed, we can take time, as it follows,

`t=(d)/(S)`

since the time was the same for the cyclist and the skater, we can create the following equation

`\begin{gathered} t_c=t_s \\ (d_c)/(S_c)=(d_s)/(S_s) \end{gathered}`

Where,

dc = 18 km

ds = 9 km

and Sc = Ss + 11

Now, we must replace and solve the equation

`(18)/(S_s+11)=(9)/(S_s)`

We need to solve for Ss as it follows,

`18S_s=\mleft(S_s+11\mright)\cdot\: 9`
`18S_s=9S_s+99`
`18S_s-9S_s=9S_s+99-9S_s`
`9S_s=99`
`(9S_s)/(9)=(99)/(9)`
`S_s=11`

Therefore, the speed of the skater is 11 kilometer per hour