# Math Help - lenght of train?

1. ## 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)

2. Hello, frigidmars!

Did you make a sketch?

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

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

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

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

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

Therefore, the train is 528 feet long.