SOLUTION: A commuter train leaves Union station in Chicago at noon. Two hours later, an Amtrak train leaves Chicago on the same track, traveling at an average speed that is 50 miles per hour

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The average speed of each train is the distance divided by the elapsed time
for each.
The first thing we can write down is

How long is each train moving at their average speeds?
The commuter train runs from noon to 3PM, so

The Amtrak runs from noon + 2 hours to 3 PM, or 2 PM to 3 PM, so

What else happens at 3 PM?
The Amtrak train is 10 miles behind the commuter train, so

Now come the vital equations:
(a)
and
(b)
Substitute for d[a]
Substitute for v[a]
Substitute for t[a]
so,

And for equation (b),
Substitute

So, now,

Now you can solve for v[c]


Since , v[a] = 80
This answers how fast each train is going
The Commuter is going 30 MPH
The Amtrak is going 80 MPH
How far from Chicago are the trains?


d[a] = 80 miles


d[c] = 90 miles