This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let's solve this! Step 1: Calculate the distance covered by the first train before the second train starts. The first train leaves at 2:00 PM and the second train leaves at 3:00 PM. This means the first train travels for 1 hour alone. Distance = Speed × Time Distance covered by Train 1 = 60 mph × 1 hour = 60 miles. Step 2: Calculate the remaining distance between the cities when both trains are moving. Total distance = 400 miles. Remaining distance = Total distance - Distance covered by Train 1 Remaining distance = 400 miles - 60 miles = 340 miles. At 3:00 PM, the trains are 340 miles apart and both are moving towards each other. Step 3: Calculate the relative speed of the two trains. Since the trains are moving towards each other, their speeds add up. Relative speed = Speed of Train 1 + Speed of Train 2 Relative speed = 60 mph + 70 mph = 130 mph. Step 4: Calculate the time it takes for them to meet after 3:00 PM. Time = Remaining distance / Relative speed Time = 340 miles / 130 mph = 34/13 hours. To convert this to hours and minutes: 34/13 hours = 2 and 8/13 hours. Minutes = (8/13) × 60 minutes ≈ 36.92 minutes. We can round this to 37 minutes for practical purposes. Step 5: Determine the exact meeting time. The trains start moving towards each other at 3:00 PM. They will meet approximately 2 hours and 37 minutes later. 3:00 PM + 2 hours = 5:00 PM. 5:00 PM + 37 minutes = 5:37 PM. The trains will meet at approximately 5:37 PM. That's 2 down. 3 left today — send the next one.