# lenght of train?

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• Oct 20th 2008, 06:56 PM
frigidmars
lenght of train?
A train traveling at 30 miles per hour reaches a tunnel which is 9 times as long as the train. If the train takes 2 minutes to completely clear the tunnel ,how long is the train?(1 mile=5280 feet)
• Oct 20th 2008, 07:58 PM
Soroban
Hello, frigidmars!

Did you make a sketch?

Quote:

A train traveling at 30 mph reaches a tunnel which is 9 times as long as the train.
If the train takes 2 minutes to completely clear the tunnel, how long is the train?

Code:

      : - L - : - - - - -9L - - - - - : - L - :       *-------*-----------------------*-------*       | Train |        Tunnel        | Train |       *-------*-----------------------*-------*               A - - - - - - 10L - - - - - - - B

The length of the train is $\displaystyle L$ feet.
The length of the tunnel is $\displaystyle 9L$ feet.
. . The train is moving from left to right.

The train enters the tunnel with its front at $\displaystyle A.$
When the train is clear of the tunnel, its front is at $\displaystyle B.$
. . It has traveled $\displaystyle 10L$ feet.

Its speed is: .30 miles/hour = 2640 feet/minute.

Using: .$\displaystyle \frac{\text{Distance}}{\text{Speed}} \:=\:\text{Time}$, we have: .$\displaystyle \frac{10L}{2640} \:=\:2$

. . Hence: .$\displaystyle 10L \:=\:52380 \quad\Rightarrow\quad L \:=\:528$

Therefore, the train is 528 feet long.