Crosswind components

In article ,
arcwi wrote:
That's simple - it's a vector sum. But can someone explane this to me:

Scenario One

An aicraft is flying from A to B, TAS=200 Kts, Distance AtoB=100nm, Wind
blowing from B to A with a speed=100Kts
Everyone should be able to claculate that GS(A-B)=100 Kts and GS(B-A)=300
Kts , therefore round trip time A-B-A=60min+20min=1hr20min

Scenario Two

Same as One, but remove the wind completely. The GS in both cases = 200 Kts,
therefore round trip time A-B-A = 30min+30min = 1hr

Can someone explain the difference?

I just wrote a long reply about how vectors sort of work. Not sure if
this helps or not (as I'm not 100% sure of the question you're trying to
ask but...).
Break it down a bit more. Thing of Scenario 1 as two trips:

A-B, flying at 200kts into 100kts head win, gs = 100kts. Distance is
100kts. 100/100 = 1hr
B-A, flying at 200kts with 100kts tail wind, gs = 300kts. Distnace is
100kts. 100/300 = 20min (1/3 of an hour)
Total time 1:20

Scenario 2:
A-B, flying at 200kts no wind. Distance is 100kts. 100/200 = 30 min
B-A, flying at 200kts no wind. Distance is 100kts. 100/200 = 30 min
Total time 1hr

Here's teh take home message, wind ALWAYS slows you down (round trip).
And you spend more time flying with a headwind than a tail wind(it's not
50/50 ^_^).