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### Speed of Two Trains

```
Date: 7/31/96 at 13:50:14
From: Anonymous
Subject: Two Trains Word Problem

This problem from my math book has haunted me for weeks...

A train leaves Chicago for Indianapolis, 216 km away, at 9 a.m.  One
hour later, a train leaves Indianapolis for Chicago.  They meet at
noon.  If the second train had started at 9 a.m and the first train at
10:30 a.m., they would still have met at noon.  Find the speed of each
train...

I know that the answer is:  First train 36km/hr, second train 54 km/hr

But how? I made the following charts:

Original Trip:            If Changes To Schedules Made:

Distance   Rate   Time               Distance  Rate   Time
Train 1  d1         r1      3        Train 1  d1        r1     1.5
Train 2  216-d1     r2      2        Train 2  216-d1    r2     3

I have plugged the answers in every which way but I can't find the
proper sequence of equations that when substituted make the answers
match... Any help in this would be greatly appreciated.  Thanks!
```

```
Date: 7/31/96 at 14:21:48
From: Doctor Robert
Subject: Re: Two Trains Word Problem

You have made a very good start.  The only thing that you haven't
realized is that once you fill out 2 of the boxes in a line, the third
one follows from relationship distance = rate * time.  In the original
trip distance(1) = 3*r1  and distance(2) = 2*r2, so that

3r1+2r2 = 216

The "changes" box gives us  1.5(r2) + 3r2 = 216

This system solves to give the answers you quote.
I hope that this helps.

-Doctor Robert,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```

```
Date: 7/31/96 at 15:53:39
From: Josephine Montiel
Subject: Re: Two Trains Word Problem

I would like to thank Dr. Robert for the fast response. I still need
clarification on one point.

At the point where you say:

"In the original trip distance (1) = 3*r1  and distance (2) = 2*r2, so
that 3r1+2r2 = 216  The "changes" box gives us  1.5(r2) + 3r2 = 216,
This system solves to give the answers you quote. "

How did you get to the point 1.5(r2)?  From my chart I can only see
1.5(r1).  I know these are related, but I can't pull it out myself, so
can you detail this part for me?

j.m.
```

```
Date: 8/1/96 at 22:58:50
From: Doctor Robert
Subject: Re: Two Trains Word Problem

My boo-boo.  You are right.  The two equations are, I think, if I
don't make another boo-boo:

3r1 + 2r2 = 216

1.5r1 + 3r2 = 216

-Doctor Robert,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Word Problems

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