Final answer:
To find the next time two fountains will squirt water together, calculate the least common multiple of their intervals. Adding this time to the initial time of 15:19, we get the next simultaneous squirting time as 18:07 (6:07 PM).
Step-by-step explanation:
The student's question deals with finding the next time two fountains, which squirt water at different intervals, will squirt together after a given time. Fountain A squirts every 24 minutes and Fountain B every 42 minutes. They both squirt together at 15:19. To find the next time they will squirt together, one would need to calculate the least common multiple (LCM) of the two intervals (24 and 42 minutes). The LCM of 24 and 42 is 168. This means the fountains will squirt together every 168 minutes.
Therefore, to find the next time they will squirt together after 15:19, we add 168 minutes to that time. Converting 168 minutes into hours gives us 2 hours and 48 minutes (since 60 minutes make an hour). Adding 2 hours and 48 minutes to 15:19 gives us 18:07 (6:07 PM) as the next time both fountains will squirt water together.