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How Long is the Train?

```
Date: 05/21/99 at 11:18:33
From: benajmin kim
Subject: Length of train

Two trains are travelling in opposite directions along parallel
tracks. Train A is travelling at 72kph and train B at 54kph. The
driver of train A notices that it takes train B eight seconds to pass
him. What is the length of train B?
```

```
Date: 05/21/99 at 12:19:16
From: Doctor Peterson
Subject: Re: Length of train

Hi, Benjamin.

Since the trains are going in opposite directions, to someone on train
A it looks as if he is standing still and the other train is going
past at 72+54 = 126 mph. Do you see why?

If it takes 8 seconds for the whole train to pass the driver, you can
calculate how far an object going 126 mph will go in 8 seconds, and
that is how long the train is.

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

```
Date: 05/21/99 at 13:53:14
From: Doctor Anthony
Subject: Re: length of train

Since the trains are travelling in opposite directions they have a
closing speed of  72 + 54 km/h  =  126 km/h = 126 x 1000/3600  m/sec

= 35 m/sec

You can think of the driver of train A as stationary and think of
train B as passing him at 126 km/hr. ( = 35 m/sec)

distance = speed x time

=  35 x 8

=  280 m

So train B is 280 metres long.

- Doctor Anthony, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra
Middle School Word Problems

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