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Math Help - Two ferry boats...

  1. #1
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    Two ferry boats...

    Two ferry boats sail back and forth across a
    river, each traveling at a constant speed, and
    turning back without any loss of time. They
    leave opposite shores at the same instant, pass
    for the first time 700 feet from one shore,
    continue on their way to the banks, return and
    pass for the second time 400 feet from the
    opposite shore. What is the width of the river?Thank you
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  2. #2
    Senior Member Sambit's Avatar
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    It is (700 + 400 - the distance covered by the slower boat between the two times they pass each other). How to find the last one remains a question...
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  3. #3
    MHF Contributor
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    Further hint: when they pass for the 2nd time, sum of distances travelled by boats = 3 times river width
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  4. #4
    MHF Contributor
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    So I can throw my "worksheet" away(!):

    Code:
    A..........a=700.............>A,B<......................................B
    
    B<............................B,A......................................>A
    .                                                                       .
    B.................................................>B,A<...b=400.........A
    Make the 2 boats A and B ; and let a =700, b = 400; let d = distance

    A:B "distance travelled" ratios:
    From 1st meeting: a / (d - a)
    From 2nd meeting: (d + b) / (2d - b)

    a / (d - a) = (d + b) / (2d - b)
    Leads to: d = 3a - b
    So distance = 3(700) - 400 = 1700

    Speeds don't matter; buy they'll be in same ratios, of course.
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