Question 389044
The trains meet somewhere between station a and station b
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let train 1 "from" station a
let train 2 "from" station b
let d1=distance train 1 travels after meeting train 2
let d2=distance train 2 travels after meeting train 1
let r1=rate of train 1
let r2=rate of train 2
let t=time when trains meet
distance =rate * time or d=r*t
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from meeting point to station a:  train 1 has travelled r1*t
and train 2 will travel 4 hours to get to station a or r2*4
so...   r1*t = r2*4
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likewise
r2*t=r1*9  
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solving for t:   r2*4/r1=t and r1*9/r2=t
4*r2/r1=9*r1/r2
4r2^2=9*r1^2   (cross multiply)
2*r2=3*r1
2*r2/3=r1
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we also know that the total distance is 300, so 
d1+d2=300
4*r2+9*r1=300
4*r2+9*(2*r2/3)=300
4*r2+6r*2=300
10*r2=300
r2=30
r1=2*r2/3=20