Train and Tunnel

Date: 07/18/2001 at 08:04:05
From: Matthew
Subject: Word Problems

A freight train 800 metres long is travelling at a constant speed of 
18km per hour. The front of the train enters a tunnel 1.6km long at 
exactly 1:00 p.m. At what time does the rear of the last carriage of 
the train emerge from the tunnel?

Date: 07/19/2001 at 13:00:59
From: Doctor Ian
Subject: Re: Word Problems

Hi Matthew,

The first thing I do with a problem like this is draw a picture, so I 
can keep track of what I know and what I need to find out. 


                              1600m
                        ())))))))))))))))
  1:00          [][][][]
                  800m 

  1:00 + t1                      [][][][]

  1:00 + t2                              [][][][]

Now, this suggests an easy way to solve the problem.  We can think of 
the train as moving its own length three times:

                        ())))))))))))))))
                 [][][][]
                         [][][][]
                                 [][][][]            
                                         [][][][]

So the last car will emerge from the tunnel at 1:00 + 3T, where T is 
the amount of time that it takes for the train to travel its own 
length.

The train moves 18,000m in 60 minutes. So how long does it take the 
train to move 800m? 

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