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Thread: lenght of train?

  1. #1
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    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)
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  2. #2
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    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 $\displaystyle L$ 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.

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