Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Trains, Speed, and Tunnels


Date: 09/10/98 at 19:16:05
From: Matthew
Subject: Trains and Tunnels

A freight train is 500m long. It passes through a tunnel 2000m long. 
Sixty seconds elapse between the time the last car enters and the time 
the engine exits the tunnel. How fast is the train traveling? 

I would probably be able to figure this out if I knew the time when the 
engine enters and exits the tunnel, but I don't know how to calculate 
the speed the way the question says. I've tried drawing a picture on 
graph paper, but it doesn't help. I hope you can help me. Thank you.


Date: 09/11/98 at 17:00:25
From: Doctor Peterson
Subject: Re: Trains and Tunnels

Hi, Matthew. It is a little tricky, but when you see it right, it's 
not too bad. Let's draw a sort of graph, with the distance through the 
tunnel along the x-axis and time along the y-axis (which I'll draw 
downward for convenience):

             tunnel
      in     2000m     out
    0+====================+--->  <-- at time 0, the last car
     |\   500m     \                 enters the tunnel
     | \            \
     |  \            \
     |   \   train    \
     |    \            \
     |     \            \
     |      \            \
   60|       \            \      <-- at time 60, the engine
     V      last         engine      exits the tunnel
             car

You could also just draw a picture of the train and tunnel at the 
start and end of the 60 seconds, to see where it is:

    ___________________________ time 0
   |500m      tunnel           |
   XXXXXX
   |___________________________|
                2000m

    ___________________________ time 60
   |          tunnel       500m|
                          XXXXXX
   |___________________________|

At time 0, the engine was 500 m into the tunnel, and at time 60 it was 
at the end. So in those 60 seconds, the engine traveled (2000 - 500) 
meters. Now can you finish the problem?

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

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/