MIA-20260531-E4D4354C

Here's how to solve this problem step-by-step: **1. Analyze the movement of the first train (from Chicago):** * **Speed:** 60 mph * **Departure Time:** 10:00 AM **2. Analyze the movement of the second train (from St. Louis):** * **Speed:** 80 mph * **Departure Time:** 11:00 AM * **Starting Position:** 300 miles south of Chicago **3. Account for the head start of the first train:** The train from Chicago has a one-hour head start before the train from St. Louis even begins moving. * **Distance covered by Chicago train in one hour:** 60 mph * 1 hour = 60 miles **4. Determine the remaining distance between the trains when both are moving:** At 11:00 AM (when the second train starts), the train from Chicago has traveled 60 miles south. This means the effective distance separating them at 11:00 AM is less than the initial 300 miles. * **Remaining distance:** 300 miles (initial distance) - 60 miles (Chicago train's head start) = 240 miles **5. Calculate their relative speed:** Since the trains are moving towards each other, their speeds add up to determine how quickly they close the distance between them. * **Relative speed:** 60 mph (Chicago train) + 80 mph (St. Louis train) = 140 mph **6. Calculate the time it takes for them to meet after 11:00 AM:** Now we need to find how long it takes for them to cover the remaining 240 miles at their relative speed. * **Time = Distance / Speed** * **Time to meet (after 11:00 AM):** 240 miles / 140 mph = 1.714 hours (approximately) **7. Convert the decimal hours into minutes:** * **Minutes:** 0.714 hours * 60 minutes/hour = 42.84 minutes (approximately, let's round to 43 minutes for practical purposes) **8. Determine the exact meeting time:** They start closing the remaining distance at 11:00 AM. Add the calculated time to this. * **Meeting time:** 11:00 AM + 1 hour + 43 minutes = 12:43 PM **Therefore, the trains will meet at approximately 12:43 PM.**