Crosswind components

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?

"James L. Freeman" wrote in message
om...
Can someone offer a non-mathematical EXPLANATION (as opposed to
DESCRIPTION) of why the speed of headwind and crosswind components of
a wind add up to more than the speed of the wind?

Thanks.