MIA-20260531-B536C7D4

To determine what time the two trains meet, we need to calculate the distance each train covers and track their positions over time. Here is the step-by-step reasoning: **Step 1: Understand the starting conditions** * The distance between Chicago and St. Louis is 300 miles. * Train 1 (Chicago) leaves at 10:00 AM traveling South at 60 mph. * Train 2 (St. Louis) leaves at 11:00 AM traveling North at 80 mph. **Step 2: Calculate Train 1's head start** Train 1 leaves exactly one hour before Train 2. During this hour, Train 2 is sitting still in St. Louis. * Distance covered by Train 1 between 10:00 AM and 11:00 AM = Speed × Time = 60 mph × 1 hour = **60 miles**. **Step 3: Calculate the remaining distance at 11:00 AM** At 11:00 AM, Train 2 begins to move. We need to find out how far apart they are at this exact moment. * Remaining distance = Total distance - Train 1's head start distance * Remaining distance = 300 miles - 60 miles = **240 miles**. **Step 4: Calculate their combined (relative) speed** From 11:00 AM onward, both trains are moving toward each other. When two objects move toward each other, their speeds add up to determine how fast the gap between them is closing. * Combined speed = Speed of Train 1 + Speed of Train 2 * Combined speed = 60 mph + 80 mph = **140 mph**. **Step 5: Calculate the time it takes to close the gap** Now we divide the remaining distance by their combined speed to find out how long it takes them to meet after 11:00 AM. * Time = Distance ÷ Speed * Time = 240 miles ÷ 140 mph = **12/7 hours** (or roughly 1.714 hours). **Step 6: Convert the time into hours and minutes** To make this readable, we convert the fraction of an hour into minutes: * 12/7 hours = 1 full hour and 5/7 of an hour. * (5/7) × 60 minutes = 300/7 minutes = **42 and 6/7 minutes** (approximately 42 minutes and 51 seconds). **Step 7: Add the travel time to the 11:00 AM start time** * Start time: 11:00 AM * Add 1 hour: 12:00 PM (Noon) * Add 42 minutes and 51 seconds: 12:42 PM and 51 seconds. **Conclusion:** The two trains will meet at exactly **12:42 and 6/7 PM** (or approximately **12:42:51 PM**).