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.

$s=\frac{d}{t}$

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,

$t=\frac{d}{S}$

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

$\begin{gathered} t_c=t_s \\ \frac{d_c}{S_c}=\frac{d_s}{S_s} \end{gathered}$

Where,

dc = 18 km

ds = 9 km

and Sc = Ss + 11

Now, we must replace and solve the equation

$\frac{18}{S_s+11}=\frac{9}{S_s}$

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$$9S_s=99$$\frac{9S_s}{9}=\frac{99}{9}$$S_s=11$

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