algabre

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the speed of the current in a river is 6 mph a ferry operator who works that part of the river is looking to buy a new boat for his business everyday his route takes him 22.5 miles against the current and back to his deck and he needs this trip in a total of 9 hours he has a boat in mind but he can only test it on a lake where there in no current how fast must the boat go on the lake in order for it to serve the ferry operators needs

can someone please explain?

  • algabre -

    (22.5/r-6)+(22.5/r+6)=9
    Multiply the equation by r^2-36.
    Resulting equation: 9r^2-45r-324=0
    Simplify: r^2-5r-36=0
    Factor: (r-9)(r+4)
    Answer: rate of ferry= 9mph

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