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Homework Help: How far will two people travel in a race?

  1. Sep 10, 2015 #1
    1. The problem statement, all variables and given/known data
    John and Fred are racing. Fred, being faster, gives john a 20 s head start. John runs at 12 km/hr (10/3 m per second) and Fred at 16 km/hr (40/9 m per second)

    How long after John starts will Fred catch him?

    How far from the start do the two meet?

    2. Relevant equations
    d = 1/2 (Vf + Vi) t

    3. The attempt at a solution
    my list of givens:
    -Vi (10/3 for John, and 40/9 for Fred)
    -Vf = 0 (for both)
    d for Fred = d for John (displacements are equal)

    what I do not know:
    -time taken

    I know that I could use kinematic equations, but I don't really know which ones to use (except for the one I wrote here) so I tried to take a very basic algebra approach to it. I figured out how far John traveled in the 20 second head start that he got (200/3 m) and then I set it up in a "solve for x" style. so:
    10/3 x +200/3 = 40/9 x, and then I got that x (time) equals 60 seconds, and then added 20 seconds (john's head start) to get that the time at which their displacements are equal is 80 s. I then plugged it back into the original equation and figured out that the distance traveled was 266.7 m until Fred caught John.
    So first off, are those values correct? and secondly, how do I do that exact problem, but instead using kinematic equations?
  2. jcsd
  3. Sep 10, 2015 #2
    I don't think Vf=0 here but it looks like you didn't use the equation anyway.

    Otherwise I think you got the right answer and you were using a kinematic equation whether you realized it or not.
  4. Sep 11, 2015 #3


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    Science Advisor
    Homework Helper
    Gold Member

    There is no acceleration involved in this problem so the kinematic equations essentially all simplify to velocity = distance / time which is what you used.
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