1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Distance Problem

  1. Feb 22, 2013 #1
    1. The problem statement, all variables and given/known data
    This problem has already been solved but i got a quite few clarifications:
    http://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.493396.html

    "a boy on his bicycle intends to arrive at a certain time to a town that is 30 km away from his home .after riding 10 km, he rested for half an hour and as a result he was obliged to ride the rest of the trip 2km/hr faster ."
    2. Relevant equations
    v = d/t
    t = d/v


    3. The attempt at a solution
    Why did he disregard the 10km?
    i think the formula should've of look like this:
    [tex]\frac{30}{s}=\frac{10}{s}+0.5+\frac{20}{s+2}[/tex]
    (total time riding on original speed for the whole trip) = (time riding on original speed (for 10km))+(time rested)+(faster velocity on the rest (for 20km))

    the formula he used:
    [tex]\frac{30}{s}=\frac{30}{s+2}+0.5[/tex]
     
    Last edited: Feb 22, 2013
  2. jcsd
  3. Feb 22, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    He has to go 20km in the time remaining after travelling 10km at the slow speed, and waiting half an hour.

    The time remaining is ##20/s = 0.5 + 20/(s+2)## ... agreeing with your formulation.

    ##40(s+2) = (s+2)s + 40s##

    rearranging:
    ##s^2+2s-80=0##

    by quadratic equation:
    ##s \in \{ 10,-8 \}##

    possible answers are 10hr and -8hr ... pick the positive one.
    This is the same answer.

    So your question is, "how did he know that his version would be correct?"
    Try plotting the velocity-time graph.
     
    Last edited: Feb 22, 2013
  4. Feb 22, 2013 #3
    The solutions to the quadratic equation are +8 and -10.
    The solution for the problem is then 8km/h.

    In the link given he is solving a different problem. I suppose he did not read the problem carefully.
     
  5. Feb 22, 2013 #4

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Did I set up the quadratic incorrectly ...

    the discriminant is 324
    so ##s =\frac{1}{2}(-2\pm\sqrt{324}=1\pm 9## ... Oh I see: I misplaced a minus sign!
    <mumble mumble grzzl>
    ... time for bed!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Distance Problem
  1. Distance Problem! (Replies: 3)

  2. Distance problem (Replies: 2)

  3. Distance Problem (Replies: 1)

  4. Distance problem (Replies: 13)

Loading...