Question

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?

Answer 1

It will take 2.2 hours

Explanation:

Answer 2

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 about:
t = 2.2 h