Word Problem Regarding Time and Distance

Date: 05/30/2002 at 00:30:27
From: Dom LaRue
Subject: Word problem regarding time and distance

This is our problem of the week and I am stumped as to how to figure 
out the answer. Here is the question: 

A train is going through a tunnel that is 650 feet long.  The train is 
traveling 100 feet per second.  The train enters the tunnel on one 
end.  Twenty-six seconds later the last car exits the other end of the 
tunnel.  How long is the train?  

I know that I took 100 feet per second and multiplied it times 26 
seconds which is 2600 feet which equals the distance of when the train 
entered the tunnel and the last car exits the tunnel.  I do not know 
what to do with the tunnel length, whether to add or subtract.  Also 
is there a way to write or describe it algebraically?  

Thank you for all your help.

Date: 05/30/2002 at 09:56:30
From: Doctor Ian
Subject: Re: Word problem regarding time and distance

Hi Dom,

Here is the situation just before the train enters the tunnel,

                    +---------------------+
      [][][][][][][>|                     |
                    +---------------------+
      |-------------|        650 ft
           L

where L represents the length of the train.  Here is the 
situation just after the last car exits the tunnel:

                    +---------------------+
                    |                     |[][][][][][][>
                    +---------------------+
                             650 ft       |--------------|
                                                 L

If '[>' is the front of the train, then in 26 seconds it moves 
(650+L) feet, right?  So

      distance = rate * time

  (650 + L) ft = (100 ft/sec) * (26 sec)

Can you take it from here?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 05/31/2002 at 10:01:24
From: Dom LaRue
Subject: Thank you (Word problem regarding time and distance)

Thank you so much for the prompt reply!  It really helped 
me fully answer the problem for math!