Question

A cyclist traveled 12 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel

Answer 1

Let v be the speed of the in-line skater, and t the time they both traveled. Applying the law $s=vt$, where s is the space, v is the velocity and t is time, we have

$45=vt$

In the same amount of time, traveling at v+12 km/h, the cyclist travels 75km:

$75=(v+12)t$

Solving both equations for t leads to

$t=\dfrac{45}{v},\quad t = \dfrac{75}{v+12}$

Since the left hand sides are equal, so must be the right hand sides:

$\dfrac{45}{v}=\dfrac{75}{v+12} \iff 45(v+12)=75v \iff 45v+540=75v \iff 30v=540$

Divide both sides by 30 to get

$v=18$