Answer:
(a) To find out how long it takes for Claudia to catch up with Cindy, we can first calculate the head start that Cindy had before Claudia started. Cindy had a head start of:
d = rt = 108 km/h x 1 h 40 min = 180 km
where d is the distance that Cindy traveled during the 1 hour 40 minutes (1.67 hours) between her departure and Claudia's departure, r is Cindy's speed, and t is the time she traveled.
When Claudia started, both Cindy and Claudia were 180 km away from Beach Town. The distance between them decreases at a rate equal to the difference in their speeds, which is:
124 km/h - 108 km/h = 16 km/h
So Claudia catches up at a rate of 16 km/h. The time it takes for Claudia to catch up is then:
t = d / r = 180 km / 16 km/h = 11.25 hours
However, we need to subtract the 1 hour 40 minutes (1.67 hours) that Cindy traveled before Claudia started to find the actual time Claudia took to catch up with Cindy:
t = 11.25 hours - 1.67 hours = 9.58 hours
Therefore, Claudia took about 9 hours and 35 minutes (0.58 x 60 minutes) to catch up with Cindy.
(b) When Claudia catches up with Cindy, they are both the same distance away from Beach Town. Cindy has already traveled 180 km when Claudia catches up, so the distance they are from Beach Town is:
600 km - 180 km = 420 km
Therefore, they were 420 km away from Beach Town when Claudia caught up with Cindy.