Final answer:
To find when two trains traveling north will meet, we calculate the time it takes for the second faster train to catch up to the first. The first train has a 3-hour head start, traveling at 50mph. The second train, traveling at 60mph and departing 3 hours later, will catch the first after 15 hours, and thus, they will meet at 8 am the next day.
Step-by-step explanation:
To solve the problem of when two trains traveling in the same direction will meet, we can apply a simple distance, rate, and time relationship. The first train leaves Los Angeles at 2 pm heading north at 50mph. By the time the second train leaves Los Angeles heading in the same direction at 60mph (3 hours later at 5 pm), the first train will have already traveled 150 miles (3 hours * 50mph).
Now, we must determine how much time it will take for the second train to catch up to the first. The second train is moving at a rate 10mph faster than the first train. Therefore, for every hour that passes, the second train decreases the gap between them by 10 miles. Starting with a 150 miles gap, we can form the equation:
10 miles/hour * t = 150 miles, where t is the time in hours needed to close the gap. Solving for t, we get t = 150 miles / 10 miles/hour = 15 hours.
Since the second train leaves at 5 pm, we add 15 hours to this departure time to find that the trains will meet at 8 am the next day. Hence, the trains will meet at 8 am the following day after the second train departs.