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### 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:
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