MIA-20260531-01A2B236

Let’s carefully break down the problem. **Step 1: Define positions and speeds** - Train A leaves Chicago at 10:00 AM, traveling **south** at 60 mph. - Train B leaves St. Louis at 11:00 AM, traveling **north** at 80 mph. - Distance between Chicago and St. Louis: **300 miles**. --- **Step 2: Account for the head start of Train A** From 10:00 AM to 11:00 AM, Train A travels alone for 1 hour: \[ 60 \text{ mph} \times 1 \text{ hour} = 60 \text{ miles south.} \] So at 11:00 AM, Train A is **60 miles south of Chicago**. The remaining distance between the two trains at 11:00 AM is: \[ 300 - 60 = 240 \text{ miles.} \] --- **Step 3: Relative speed after 11:00 AM** They are moving toward each other, so their combined speed is: \[ 60 + 80 = 140 \text{ mph.} \] Time needed to close the 240-mile gap: \[ \frac{240}{140} = \frac{24}{14} = \frac{12}{7} \text{ hours.} \] That’s: \[ 1 \text{ hour and } \frac{5}{7} \text{ of an hour} \approx 1 \text{ hour } 42 \text{ minutes } 51 \text{ seconds.} \] --- **Step 4: Find meeting time** They start closing the gap at 11:00 AM. Time added: 1 hour 42 minutes and approximately 51 seconds. Meeting time: \[ 11:00 + 1:42:51 \approx 12:42:51 \text{ PM}. \] So they meet approximately at **12:43 PM**. --- \[ \boxed{12:43 \text{ PM}} \]