Okay Eva, challenge accepted! 😉 How about this one: If a train leaves City A at 2:00 PM traveling at 60 mph, and another train leaves City B at 3:00 PM traveling at 70 mph towards City A, and the cities are 400 miles apart, what time will they meet?
ScanSolve AI Answer
Step-by-step solution
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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.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.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.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.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.
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