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Math Help - [SOLVED] Train Problem

  1. #1
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    [SOLVED] Train Problem

    A car cruising at 65 mph, passes a train from the back to the front, in 2 minutes. At the same instant, another car, that is also traveling at 65 mph, moves from the front of the back of the train in 10 seconds. If the train's speed is constant, what is the length of the train?
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  2. #2
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    Train Problem

    let speed of the train be v mph, & length of the train be L mi,
    2 min = 1/30 h & 10 sec = 1/6 min = 1/360 h, so

    L = (65 - v) /30 ....... [ I ]

    L = (65 + v) / 360 ... [ II ]

    (65+v)/(65-v) = 360/30 = 12
    65+v = 780 - 12v
    13v = 715
    v = 55 mph

    L = (65 - 55) 30 = 1/3 mi
    = 5280/3 ft
    = 1760 ft

    ans: 1760 ft
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  3. #3
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    Lexington, MA (USA)
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    Hello, warriors837!

    You are correct . . . Good work!

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  4. #4
    Newbie
    Joined
    Nov 2009
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    Please explain :-]

    I am a real novice at this, could someone please explain the step by step properties used to solve this problem. I got 'lost' after the first two discriptions of L.
    I, in a round about way was able to 'guess' the speed of the train [as less than that of the first car] and determine it's length. But I was only guessing at the speed of the train, I couldn't prove it. thanks in advance.
    txt
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