i dont get this help?

The speed of a stream is 3 mph. A boat travels 11 miles upstream in the same time it takes to travel 17 miles downstream. What is the speed of the boat in still​ water?

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  • 2 months ago

    Let v mph be the speed of the boat in still water.

    17/(v+3)=11/(v-3)

    =>

    17(v-3)=11(v+3)

    =>

    17v-51=11v+33

    =>

    6v=84

    =>

    v=14 mph.

  • Philip
    Lv 6
    2 months ago

    d = rt. distance = rate*time. Stream rate = 3 mi/h. Put boat's rate in still water = bmi/h 

    Against the stream: d =11 mi, r = (b-3) mi/h, t against stream = ta = [11mi/(b-3)](h/mi).

    With the stream: d = 17 mi, r = (b+3) mi/h, t with stream = tw = [17mi/(b+3)](h/mi).;

    Now ta = tw. ie., 11/(b-3) = 17/(b+3),ie., 11(b+3) = 17(b-3), ie., 33+51= 6b, ie., b =14.

    Boat's rate in still water = 14 mi/h.  

  • 2 months ago

    LET THE SPEED IN STILL WATERS BE  X

    UPSTREAM SPEED = X-3   mph

    DOWNSTREAM SPEED = X+3   mph

    TIME TAKEN = 11/ (X-3) =  17/ (X+3)

    CROSS MULTIPLY

    17X-51 = 11X+33

    6X= 84

    X = 14 mph ANSWER

    CHECK

    11/ (14-3) = 17/ ( 14+3) = 1 HOUR

  • 2 months ago

    Recall: s = d/t → where s is the speed, d is the distance, t is the time

    Sb: speed of the boat

    Sc: speed of the current = 3 mph

    The case downstream (17 miles).

    The speed of the boat and the speed of the current are in the same direction.

    You can add these speeds together.

    s = d/t

    Sb + Sc = d/t → where: d = 17 miles and where: Sc = 3 mph

    Sb + 3 = 17/t

    t = 17/(Sb + 3)

    The case upstream (11 miles).

    The speed of the boat and the speed of the current are opposite, so you make the difference.

    s = d/t

    Sb - Sc = d/t → where: d = 11 m and where: Sc = 3 mph

    Sb - 3 = 11/t

    t = 11/(Sb - 3) → given that the time is the same → recall: t = 17/(Sb + 3)

    11/(Sb - 3) = 17/(Sb + 3)

    11.(Sb + 3) = 17.(Sb - 3)

    11Sb + 33 = 17Sb - 51

    - 6Sb = - 84

    Sb = 14 mph ← this is the speed of the boat in still water

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  • 2 months ago

    The speed of a stream is 3 mph. 

    A boat travels 11 miles upstream in the same time 

    it takes to travel 17 miles downstream. 

    Let x be the speed of the boat in still​ water.

    11/(x - 3) = 17/(x + 3)

    11(x + 3) = 17(x - 3)

    6x = 33 + 51

    x = 84/6 = 14

    The speed of the boat in still​ water is 14 mph.

  • sepia
    Lv 7
    2 months ago

    The speed of a stream is 3 mph. 

    A boat travels 11 miles upstream in

    the same time it takes to travel 17 miles downstream. 

    What is the speed of the boat in still​ water?

    Let the speed of the boat in still water be x mph. 

    As the speed of the stream is 3 mph, 

    upstream speed will be ( x − 3) mph

    and downstream speed will be (x + 3) mph. 

    The time taken by the boat for traveling 11 miles upstream will be  11/x − 3 

    and time taken by the boat for traveling 17 miles downstream is  17/x + 3. 

    As the two are equal 11/(x − 3) = 17/x + 3

    Hence

    17(x - 3) = 11(x + 3). 

    6x = 84

    Hence x = 14.

  • 2 months ago

    Let the speed of the boat be v m.p.h

    Against the stream we have:

    (v - 3)t = 11

    With the stream we have:

    (v + 3)t = 17

    so, 11/(v - 3) = 17/(v + 3)

    => 11(v + 3) = 17(v - 3)

    i.e. 11v + 33 = 17v - 51

    so, 6v = 84

    Hence, v = 14 m.p.h

    Then, (14 - 3)t = 11

    i.e. t = 1 hour

    Total journey 2 hours

    :)>

  • vaklas
    Lv 4
    2 months ago

    This should be in the Physics Section but once again it is proven that maths are behind everything.

    Assume that the boat in still water travels with speed v mph. If it travels downstream, it takes advantage on the speed of the stream and travels with  v + 3 mph. If it travels upstream it loses some speed from the opposite direction of the stream, hence v - 3 mph.

    Since v + 3 = 17, and v - 3 = 11, you can see that the speed of the boat in still water (if the stream speed was 0) would be 14 mph.

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