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Math Help - Word Problem Help

  1. #1
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    Word Problem Help

    I need help with this stupid word problem. I'm at my girlfriend house and I left my book at home.

    A stream flows at a rate of 4 mph. A boat travels 70 miles downstream and returns in a total time of 6 hrs. What is the speed of the boat in still water.

    I am a complete retard when it comes to word problems. Can someone at least point out how I can get the correct formula for this?
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  2. #2
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    Hi, I do not know if this is correct or not but this is going to be my best guess.

    The boat travels for 6 hours and the stream flows at 4 mph.

    In total that would be 24 MPH?

    70-24=46 Mph


    Not sure if it's correct as I said above but I think it should be.


    EDIT: mine is completely wrong didn't see that it said STILL water.
    Last edited by simoonlu; December 8th 2010 at 10:07 PM.
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  3. #3
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    Hello, BuhRock!

    A stream flows at a rate of 4 mph.
    A boat travels 70 miles downstream and returns in a total time of 6 hrs.
    What is the speed of the boat in still water?

    We know that: . \text{(Distance)} \:=\:\text{(Speed)} \times \text{(Time)} \quad\Rightarrow\quad T \:=\:\dfrac{D}{S}

    Let \,b = speed of the boat in still water.


    Going downsream (with the current), the boat's speed is: . b + 4 mph.
    To go 70 miles downsteam, it takes: \dfrac{70}{b+4} hours.


    Going upstream (against the current), the boat's speed is: . b - 4 mph.
    To go 70 miles upstream, it takes: \dfrac{70}{b-4} hours.


    The total time is six hours.
    There is our equation! . . . . . \dfrac{70}{b+4} + \dfrac{70}{b-4} \:=\:6


    Multiply by (b+4)(b-4)\!:\;\;70(b-4) + 70(b+4) \:=\:6(b+4)(b-4)

    . . which simplifies to: . 3b^2 - 70b - 48 \:=\:0

    . . which factors: . (b-24)(3b + 2) \:=\:0

    . . and has roots: . b \:=\:24,\:-\frac{2}{3}


    The boat's speed in still water is: . 24\text{ mph.}

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