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)

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- Oct 20th 2008, 06:56 PMfrigidmarslenght 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 PMSoroban
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.