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Math Help - 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 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.

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