If there is a straight section of highway 120 Km between them and Joe travels south towards Bob at 30Kph
while Bob travels north towards Joe at 25Kph, how long will it be before they meet and how far will each have traveled in that time?
(d=r/t where d is distance, r is rate and t is time)

Please show all of your work and if possible write a program that solves the problem for any given rates and distances.
Thanks for participating and sharing, please invite your friends who might be interested. I ♥ Math for programming! -JpE-

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:: program at bottom ::
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Given:	t1 = 0h
		t2 = 0h
		v1 = 30 km/h
		v2 = 25 km/h
		s1(t1) = 0 km
		s2(t1) = 120 km

Wanted:	s(t)
	t

		     a(joe)                                      b(bob)
		-----•.--------------------------•----------------•-.----
		    s(t1)                      s(t)             s(t1)
		     ---> v1                                v2 <--

Solution:

______________________________________________________
(1) ERB Joe

Δs1(t1, t) = s1(t) - s1(t1)
     s1(t) = s1(t1) + Δs1(t1, t)
	 s1(t) = s1(t1) + v1.Δt(t1, 1)
	 s1(t) = s1(t1) + v1.(t-t1)
	 s1(t) = 0 km + 30 km/h.(t-0h)
	 s1(t) = 30 km/h . t

______________________________________________________
(2) ERB Bob

Δs2(t2, t) = s2(t) - s2(t2)
     	s2(t) = s2(t2) + Δs2(t2, t)
	s2(t) = s2(t2) + v2.Δt(t2, 1)
	 s2(t) = s2(t2) + v2.(t-t2)
	 s2(t) = 120 km + -25 km/h.(t-0h)
	 s2(t) = 120 km - 25 km/h . t

______________________________________________________
(3) s1(t) = s2(t)    (meeting point)
    30 km/h . t = 120 km - 25 km/h . t
	55 km/h . t = 120 km
	          t = 120 km / 55 km/h
		  t = 2,181818 h (2h 10m 54s)

______________________________________________________
(4) distance Joe

s1(t) = 30 km/h . t
      = 30 km/h . 2,181818h
	  = 65,454545 km

______________________________________________________
(5) distance Bob

s2(t) = 25 km/h . t
      = 25 km/h . 2,181818h
      = 54.545454 km


I ♥ Math for programming!
~Robin "yugecin" Claerhout

-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯-¯

:: Batch program for calculating solution ::
http://pastebin.com/yEUtQQYH
(time function not working properly (yet))
To solve this question:
Joe:
	Starting distance: 0
	Starting time: 0
	Speed: 30
Bob:
	Starting Distance: 120
	Starting time: 0
	Speed: -25   (negative because Bob is travelling to Joe)

Output:
Meeting time: 2,181 h
Distance Joe: 65.430 km
Distance Bob: 54.525 km