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Math Help - Boat Speed Word Problem - Help

  1. #1
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    Boat Speed Word Problem - Help

    The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water?

    ----------- distance--- r ----t
    Upstream ---- 45 mi -- r-3---t1
    Downstream - 45 mi ---r+3---t2
    Total Time = ----------------8 hr.

    t1=45/r-3, t2=45/r+3, t1 +t2 = 8

    45/r-3 + 45/r+3 = 8

    Multiply both sides of the equation with (r-3)(r+3)

    45(r+3)+45(r-3)=8(r-3)(r+3)
    45r + 135+45r-135=8r^2-72
    90r=8r^2-72
    90r-90r=8r^2-90r-72
    0=8r^2-90r-72
    2(4r^2-45r-36)=0
    (-r+12)(-4r-3)=0
    -r+12=0, -4r-3=0
    -r=-12, -4r=3
    (-1)-r= -12(-1)
    r=12

    -4r=3
    -4r/-4=3/-4
    r= -3/4

    So the original question was the speed of the boat in still water.
    1) Did I do the computations correctly?
    2) When I plug in the answers into the equation, it comes out correctly. So the speed of the boat in still water is ??
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  2. #2
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    Quote Originally Posted by mcruz65 View Post
    The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water?

    ----------- distance--- r ----t
    Upstream ---- 45 mi -- r-3---t1
    Downstream - 45 mi ---r+3---t2
    Total Time = ----------------8 hr.

    t1=45/r-3, t2=45/r+3, t1 +t2 = 8

    45/r-3 + 45/r+3 = 8

    Multiply both sides of the equation with (r-3)(r+3)

    45(r+3)+45(r-3)=8(r-3)(r+3)
    45r + 135+45r-135=8r^2-72
    90r=8r^2-72
    90r-90r=8r^2-90r-72
    0=8r^2-90r-72
    2(4r^2-45r-36)=0

    2(4r + 3)(r - 12) = 0

    r=12 is the only valid solution ... speed > 0
    ...
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  3. #3
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    0=8r^2-90r-72

    (-b√(b^2-4ac))/2a

    (-(-90)√((-90)^2-4(8)(-72) ))/2(8)

    (90√(8100-4(-576) ))/16

    (90√(8100+2304))/16

    (90√10404)/16

    (90102)/16

    90/16+102/16=5.625+6.375=12

    r=12
    Is this the proper way of doing this exercise?
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  4. #4
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    ... it's one way of doing it.
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