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Where would the Two Trains Meet?


Date: 5 Jun 1995 13:24:23 -0400
From: J. Poholsky's grade6A Charles River
Subject: Where would the Trains Meet?

Hello Mr.math,

Do you really do this for a living? I mean what kind of a living is that?
You sit around a computer typing all day?! Don't you get lonely? I'd simply
hate it. O.K. here's a math problem, you have 2 trains, 1 train left
Baltimore at 6:00 pm and is travelling 19 m.p.h. Yes we understand that's a
little slow, but this is a math problem. The other train left from
Philadelphia in the opposite direction and is going 85. Yes this is fast, but
it is a math problem.  Where would they meet?


Date: 6 Jun 1995 11:09:22 -0400
From: Dr. Ken
Subject: Re: Where would the Trains Meet?

Hello there!

>Do you really do this for a living? I mean what kind of a living is that?
>You sit around a computer typing all day?! Don't you get lonely? I'd simply
>hate it. 

Well, to each his or her own then.  Actually, you may be surprised to learn
that none of the doctors of math is paid for this, we do it on a volunteer
basis.  Since we divide the work among a few different people, nobody has to
sit around a computer all day, we each sit around a computer for just a
little while.  And it's fun, darnit!

>O.K. here's a math problem, you have 2 trains, 1 train left
>Baltimor at 6:00 pm and is traveling 19 m.p.h. Yes we understand that's a
>little slow, but this is a math problem. The other train left from
>Philedalphia in the opposite direction and is going 85. Yes this is fast but
>it is a math problem. Where would they meet?
 
Picture what's happening in this problem.  You've got two trains speeding
toward each other, one going 85 mph and the other going 19 mph.  So their
total speed, relative to each other, is 85 mph + 19 mph = 104 mph.  I don't
know exactly how far apart these two cities are from each other (although I
made the drive between Baltimore and Philly just yesterday!), so I'll denote
that distance by the letter D.  You can find out how far it is and just fill
it in.

If the total speed is 104 mph, then let the time the two trains travel be t.
Then since Distance = Rate x Time, we get 
D = 104t, so t = D/104.  This tells you _when_ the trains meet, and to find
out _where_ they meet you would take t and use the formula Distance = Rate x
Time again.  Hope this helps!  Thanks for the question.

-K
    
Associated Topics:
Middle School Word Problems

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