Quant - Work Rate Distance - Combining/Substracting Rates

GRE Quant Problem Solving
1

Hello everyone,
In relation to GRE Quant Concept Series focusing on work rate distance, I struggle in understanding why in some specific situations rates have to be combined or substracted.
In the practice video of a problem :
1/Greg explained the illustration where two trains go in opposite direction, why should we combine the rates ?
2/In the illustration when train has to catch up with another train heading the same direction, why should we subtract the rates ? wouldnt this be the same objective, therefore combining the rates ?

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Thank you for your help

2

Because they are in opposite direction, so both trains are coming closer to each other. If they were in the same direction, then you’d subtract, since most of the “speed” covered is common, and hence we only look at the “additional” speed one train has compared to the other (as that’s how the faster train will catch up).