Abicyclist 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
 
 It will take the second cyclist to catch up to the first cyclist about:
 t = 2.2 h