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

Sorry.  Bad typing fingers.

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