Problem
Two trains A and B start from two points P1 and P2 respectively at the same time and travel towards each other. The difference between their speed is 10 kmph and train A takes one hour more to cover the distance between P1 and P2 as compared to train B. Also by the time they meet, train B has covered 200/9 km more as compared to train A. What is the distance between P1 and P2?
Progress
In my attempt I have these. Consider u and v be the speed of train A and B respectively. and train A travels x distance and train B travels y distance before they meet. Also train A takes time t1 to reach point P2 and train B takes t2 to reach point P1. and d be the total distance between P1 and P2: y = x + 200/9, d = x + y, t2 = t1 - 1, v - u = 10.. with these information, all i can find is total time taken when they meet, which would be equal to 20/9 hrs.
Answer
You have three equations in three unknowns: $$\frac du = \frac dv +1\\ v-u=10\\ \frac {20}9(u+v)=d$$ The third seems to be the one you are missing. It comes from the fact that when they meet, the total of the distances traveled is the whole distance from $P1$ to $P2$
Added: $$v+u=\frac{9d}{20}\\v=\frac{9d}{40}+5\\u=\frac{9d}{40}-5\\d(v-u)=10d=uv\\10d=\frac {81d^2}{1600}-25\\d=200 (or -\frac{200}{81})$$
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