How would you identify what to take from a word problem to put into a quadratic equation?

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1st of all I have lived in Grayslake.  It is all one word, and it is about 50 miles from Chicago.  Enough about Geography lets do math.

Sometimes it is easier if you create a table to write the things you know about this problem, but this format is difficult to do on this site.  Another thing you can do is to draw a picture, which again doesnt' work well on the web, but I will write it out.

The first thing I notice is I don't know the speeds of the trains but they express the speed of the express train in terms of the local.  I also don't know how long it took for them to get to Chicago, but again the express train arrives an hour before the local train.  If I could find out how long it took for each train to arrive in Chicago, I could divide 50 miles by that time and get an answer.  But first I need some variables, and since I don't like using fractions, I will pick the local train since expressing the express trains speed is twice the local trains speed, and I don't end up with one half.

Let v = speed of local train so the speed of the express train is 2v.

If t is the time it takes for the local train to get to Chicago, then t-1 is the time it takes the express train to travel to Chicago.  Since they both travel the same distance (50 miles) I get:

v*t = 2v*(t-1)   Since v cancels out I get t = 2(t-1)

Solving for t I get t = 2t - 2, -t = -2, and finally t = 2 hours.

Since I know the distance traveled this gives v = 50miles/2hours = 25 mi/hr  for the local train and twice 25 =  50 mi/hr for the express train.

My answer is 25 mi/hr for the local train, and 50 mi/hr for the express train.

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