MIA-20260531-452E00EC

Here is the step-by-step reasoning to solve this problem: **Step 1: Determine the head start distance of the first train.** The first train leaves Chicago at 10:00 AM, while the second train doesn't leave St. Louis until 11:00 AM. This means the first train has a 1-hour head start. * Distance = Speed × Time * Distance traveled by Train 1 in 1 hour = 60 mph × 1 hour = **60 miles** **Step 2: Calculate the remaining distance between the trains at 11:00 AM.** The total distance between Chicago and St. Louis is 300 miles. Since Train 1 has already traveled 60 miles south by the time Train 2 starts, we need to subtract that from the total distance. * Remaining distance = 300 miles - 60 miles = **240 miles** **Step 3: Calculate the combined (closing) speed of the two trains.** At 11:00 AM, both trains are now moving toward each other. When two objects move toward each other, their speeds add together to determine how fast they are closing the gap. * Closing speed = Speed of Train 1 + Speed of Train 2 * Closing speed = 60 mph + 80 mph = **140 mph** **Step 4: Calculate the time it takes to close the remaining distance.** Now we divide the remaining distance by the closing speed to find out how long they travel before meeting. * Time = Distance ÷ Speed * Time = 240 miles ÷ 140 mph = **12/7 hours** (or approximately 1.714 hours) **Step 5: Convert the time into hours and minutes.** To convert 12/7 hours into a more readable format: * 12/7 hours = 1 whole hour and 5/7 of an hour. * To convert 5/7 of an hour into minutes, multiply by 60: * (5/7) × 60 = 300/7 minutes ≈ **42.86 minutes** (or 42 minutes and 51 seconds) **Step 6: Add this travel time to the 11:00 AM starting point.** * Start time: 11:00 AM * Add 1 hour: 12:00 PM * Add 42.86 minutes: **12:42:51 PM** **Answer:** The two trains will meet at approximately **12:43 PM** (exactly at 12:42:51 PM).