How far will two people travel in a race?

[DeathEater]

Homework Statement

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?

Homework Equations

d = 1/2 (Vf + Vi) t

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
-displacement

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?

 

[paisiello2]

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.

 

[CWatters]

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