Train and Tunnel

Date: 7/18/96 at 7:32:4
From: Anonymous
Subject: Train, Tunnel Length

A train passes completely through a tunnel in 5 minutes. A second 
train, twice as long, passes through the tunnel in 6 minutes. If both 
trains are traveling at the same speed, 24km/h, determine the length 
of the tunnel and the lengths of the trains.

Date: 7/22/96 at 21:58:24
From: Doctor Luis
Subject: Re: Train, Tunnel Length

 To answer this question you must first define what is meant by a 
train "passing through a tunnel." Thus, in order to solve this, I will 
assume that the time it takes for the train to pass through the tunnel 
is the time interval measured from the instant the front of the train 
enters the tunnel to the instant the back of the train leaves the 
tunnel. 

What is the distance traveled by the front while the train goes
"through" the tunnel?  Answer: T+L, where L is the length of the
train, and T is the length of the tunnel (this is because when the 
back leaves the tunnel, the front is L meters away from the back).

So, the first train (length l) passes the tunnel (length T) in 5 
minutes, at 24 km/hr. The distance covered (by the front) is

    (24 km/hr)*(5 mins)*(1/60 hr/mins)*(1000 m/km) = 2000 m

Therefore, T + l = 2000 m

The second train (length 2*l) passes the tunnel (length T) in 6 
minutes, at 24 km/hr. The distance covered (by the front) is

    (24 km/hr)*(6 mins)*(1/60 hr/mins)*(1000 m/km) = 2400 m

 Therefore, T + 2l = 2400 m

 Now, we have two equations in two unknowns,

  T + l = 2000
  T +2l = 2400

 from which the solution follows ( I get:  T = 1600 m, l = 400 m )


-Doctor Luis,  The Math Forum
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