A bicyclist heads east at 19 km/h. After she has traveled 24.2 kilometers, another cyclist sets out in the same direction going 30 km/h. About how long will it take the second cyclist to catch up to the first cyclist?

The generic equation of movement for this case is:

r = v * t + ro

Where,

v: speed

t: time

ro: initial position

We write the equation for each cyclist,

For Cyclist A:

r = 19 * t + 24.2

For cyclist B:

r = 30 * t

Equating equations we have:

19 * t + 24.2 = 30 * t

Clearing t:

t = 24.2 / (30-19)

t = 2.2 h

Answer:

It will take the second cyclist to catch up to the first cyclist а bout:

t = 2.2 h