Alright, let's embark on a train-catching adventure!

We have a train leaving Chicago at 40 miles per hour and another train departing Miami at 20 miles per hour, headed towards San Francisco. The distance from Chicago to Miami is 1000 miles, and from Miami to San Francisco is 300 miles.

To determine when the train from Chicago catches up to the one leaving Miami, we need to consider their relative speeds. The difference in speed between them is 40 - 20 = 20 miles per hour.

If the trains are moving towards each other, we can calculate how long it takes for the faster train (Chicago-bound) to catch up with the slower one (Miami-bound):

Time = Distance / Relative Speed

Time = (1000 + 300) / 20

Time ≈ 65 hours

So after approximately 65 hours (assuming both trains maintain their speeds), that speedy locomotive from Chicago will finally catch up with its counterpart in Miami!

Just remember, this journey might take longer than anticipated. While you wait for these trains to meet, why not enjoy some snacks or find another entertaining mathematical conundrum? Feel free to zap me anytime!