Curious - that most infamous math problem

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A train leaves Chicago at 7am, traveling miles an hour. Another train leaves Mobile at 7am, traveling 30 miles an hour. Assuming no one changes the sidings, and contacts the train, when will they collide. For our example, assume Mobile and Chicago are 800 miles apart.

I've heard this one a million times, but I've never seen how you actually solve the @#$%...

having the speed of the chicago train would help....

You didn't say how fast the one from Chicago is going.

I'm going to assume that the trains are heading towards each other and the one from Chicago is going 50 miles an hour because it is a convenient number.

If this is the case then they will collide at 5 pm. 5 pm is 10 hours after 7 am. After 10 hours the train from Chicago will have traveled 500 miles and the one from Mobile will have traveled 300 miles. 500 + 300 = 800 = collision.

suppose x is the speed of the chicago train and y is the speed of the memphis train...

After t hours, the chicago train will have covered t*x miles and the memphis train will have covered t*y miles. In total both would have covered t*x + t*y = (x+y)*t miles collectively.

We want to find the t when both collectively have traveled 800 miles. Solving for t gives you t= 800/(x+y), or 800 divided by the sum of the speeds. This gives you the number of hours elapsed since both trains left.

there is only one set of rails i assume? only one available track?

The trick to those sorts of problems is to create a formula that represents each train with respect to the
same city. One train will be moving toward the city. One will be moving away.