MIA-20260531-8BD50E83

Here's a step-by-step breakdown of the solution: **1. Understand the setup** - Distance between Chicago and St. Louis: `300 miles` - Train 1 (Chicago): Speed = `60 mph`, Departs at `10:00 AM` - Train 2 (St. Louis): Speed = `80 mph`, Departs at `11:00 AM` - Since Train 2 heads north and Train 1 is coming from Chicago (which is north of St. Louis), they are traveling **toward each other** along the same route. **2. Account for the head start** Train 1 leaves 1 hour before Train 2. - Distance covered by Train 1 from 10:00 AM to 11:00 AM: `60 mph × 1 hour = 60 miles` - Remaining distance between the two trains at 11:00 AM: `300 miles - 60 miles = 240 miles` **3. Calculate the closing speed** Because they are moving toward each other, their relative (closing) speed is the sum of their individual speeds: - `60 mph + 80 mph = 140 mph` **4. Find the time until they meet (after 11:00 AM)** - Time = Distance ÷ Speed - `Time = 240 miles ÷ 140 mph = 24/14 = 12/7 hours` **5. Convert `12/7 hours` to hours, minutes, and seconds** - `12/7 = 1 + 5/7 hours` - `5/7 hour × 60 minutes/hour = 300/7 ≈ 42.857 minutes` - `0.857 minutes × 60 seconds/minute ≈ 51.4 seconds` - So, `12/7 hours = 1 hour, 42 minutes, and 51.4 seconds` **6. Add this time to 11:00 AM** - `11:00:00 AM + 1 hour = 12:00:00 PM (noon)` - `12:00:00 PM + 42 minutes 51.4 seconds = 12:42:51 PM` ✅ **Final Answer:** The trains meet at **12:42:51 PM** (approximately **12:43 PM**). *(Note: If exact fractional form is preferred, the meeting time is exactly 12:42 and 6/7 minutes PM.)*