Results 1 to 5 of 5

Math Help - Speed of the Boat in Still Water

  1. #1
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Speed of the Boat in Still Water

    The speed of a stream is 3 mph. A boat travels 5 miles upstream in the same time it takes to travel 11 miles downstream. What is the speed of the boat in still water?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2007
    Posts
    96
    Speed up stream = x -3 (-3 because the stream movement will be negative in relation to the boat) and the boat will travel 5 miles

    x-3=5

    x=5+3

    x=8

    You can check using the other data.
    Speed down stream = x+3 (because the stream and boat movement will add) and the boat will travel 11 miles

    x+3=11

    x=11-3

    x=8

    Now you see, the boat -on still water- travels at 8 mph.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    perfectly done............

    Quote Originally Posted by Alienis Back View Post
    Speed up stream = x -3 (-3 because the stream movement will be negative in relation to the boat) and the boat will travel 5 miles

    x-3=5

    x=5+3

    x=8

    You can check using the other data.
    Speed down stream = x+3 (because the stream and boat movement will add) and the boat will travel 11 miles

    x+3=11

    x=11-3

    x=8

    Now you see, the boat -on still water- travels at 8 mph.
    Your answer is wonderfully simple.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,751
    Thanks
    651
    Hello, magentarita!

    Another approach . . .

    We'll use: . \text{Distance} \:=\:\text{Speed} \times \text{Time} \quad\Rightarrow\quad T \:=\:\frac{D}{S}


    The speed of a stream is 3 mph.
    A boat travels 5 miles upstream in the same time it takes to travel 11 miles downstream.
    What is the speed of the boat in still water?
    Let x = boat's speed in still water.


    Going upstream, the current works against the boat. .The boat's speed is x - 3 mph.
    . . It went 5 miles at x-3 mph. .This took: . \frac{5}{x-3} hours.

    Going downstream, the current works with the boat. .The boat's speed is x+3 mph.
    . . It went 11 miles at x+3 mph. .This took: . \frac{11}{x+3} hours.


    These two times are equal: . \frac{5}{x-3} \:=\:\frac{11}{x+3}\quad\hdots\quad There!

    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    ok............

    Quote Originally Posted by Soroban View Post
    Hello, magentarita!

    Another approach . . .

    We'll use: . \text{Distance} \:=\:\text{Speed} \times \text{Time} \quad\Rightarrow\quad T \:=\:\frac{D}{S}

    Let x = boat's speed in still water.


    Going upstream, the current works against the boat. .The boat's speed is x - 3 mph.
    . . It went 5 miles at x-3 mph. .This took: . \frac{5}{x-3} hours.

    Going downstream, the current works with the boat. .The boat's speed is x+3 mph.
    . . It went 11 miles at x+3 mph. .This took: . \frac{11}{x+3} hours.


    These two times are equal: . \frac{5}{x-3} \:=\:\frac{11}{x+3}\quad\hdots\quad There!
    What can I say? Your replies indicate that you are a teacher or were a teacher at one time.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: January 31st 2011, 05:12 AM
  2. Speed of Boat in Still Water
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 4th 2008, 07:16 PM
  3. Boat in Still Water
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 28th 2008, 03:15 PM
  4. Boat in Still Water
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 28th 2008, 09:08 AM
  5. boat in water, force vectors
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: April 11th 2007, 08:45 PM

Search Tags


/mathhelpforum @mathhelpforum