Results 1 to 7 of 7

Math Help - A cyclist travels 40 km at a speed x km/h. Find the time taken in terms of x etc.

  1. #1
    Junior Member
    Joined
    Jan 2011
    Posts
    49

    A cyclist travels 40 km at a speed x km/h. Find the time taken in terms of x etc.

    Hello! I would like some help with this task.

    A cyclist travels 40 km at a speed x km/h. Find the time taken in terms of x. Find the time taken when his speed is reduced by 2 km/h. If the difference between the times is 1 hour, find the orginal speed, x km/h.

    Thank you!
    Last edited by mr fantastic; February 1st 2011 at 12:27 PM. Reason: Re-titled.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by Anna55 View Post
    Hello! I would like some help with this task.

    A cyclist travels 40 km at a speed x km/h. Find the time taken in terms of x. Find the time taken when his speed is reduced by 2 km/h. If the difference between the times is 1 hour, find the orginal speed, x km/h.

    Thank you!
    Hi Anna55,

    Using rt=D, we first have:

    xt=40

    t=\dfrac{40}{x}

    After decreasing the rate by 2 km/h, we have:

    (x-2)t=40

    t=\dfrac{40}{x-2}

    The difference in time is 1 hour. So...

    \dfrac{40}{x-2}-\dfrac{40}{x}=1

    Can you finish up?
    Last edited by masters; February 1st 2011 at 12:49 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2011
    Posts
    49
    Thank you. I understand everything except why you are doing this (x+2)t=40 when is speed are reduced by 2km/h.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by Anna55 View Post
    Thank you. I understand everything except why you are doing this (x+2)t=40 when is speed are reduced by 2km/h.
    I misread your problem. Just change the + to a -. And reverse the order of the subtraction. Sorry! I'll edit my post so you can see.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2011
    Posts
    49
    Thank you! I tried to solve the equation, however I cannot. First I extended the denominator so every fraction hade the same denominator (x-2) x. After that I moved over 1 to the left side so everything equaled 0. After that I cannot continue. Can you please show me.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by Anna55 View Post
    Thank you! I tried to solve the equation, however I cannot. First I extended the denominator so every fraction hade the same denominator (x-2) x. After that I moved over 1 to the left side so everything equaled 0. After that I cannot continue. Can you please show me.
    Hi Anna55,

    Sorry for the confusion initially. Here is the complete solution.

    \dfrac{40}{x-2}-\dfrac{40}{x}=1

    Multiply each side by x(x-2)

    40x-40(x-2)=x(x-2)

    40-40x+80=x^2-2x

    x^2-2x-80=0

    (x-10)(x+8)=0

    \boxed{x=10}

    Disregard the negative solution.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Jan 2011
    Posts
    49
    Thank you very much masters! I understand everything now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Speed-Time Graph 2
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: September 14th 2011, 02:55 PM
  2. Speed-Time Graph
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: September 14th 2011, 02:52 PM
  3. Speed and Time problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: August 8th 2011, 11:13 AM
  4. The Speed of Time
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: June 30th 2010, 04:19 PM
  5. Help with speed/distance/time and d/dx?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 8th 2008, 02:55 AM

Search Tags


/mathhelpforum @mathhelpforum