Question

A cyclist traveled 12 kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel
75 kilometers, the skater had gone 45 kilometers. Find the speed of the skater.

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

$v=18$

Answer 2

Using the distance - speed relationship, the speed of the skater is calculated to be 18km/hr

Representing the scenario thus :

• Speed of skater = v
• Speed of cyclist = v + 12

Recall ::

• Time = distance ÷ Speed

In time, t :

• Skater's distance = 45
• Cyclist's distance = 75

Skater's time = (45 / v) ----(1)

Cyclist's time = (75/(v+12))----(2)

Equating (1) and (2)

(45/v) = (75/(v+12))

Cross multiply

(v + 12)45 = 75v

45v + 540 = 75v

540 = 75v - 45v

540 = 30v

v = 540 / 30

v = 18

Therefore, Skater's speed is 18 km/hr.

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