For red it's obvious, since half of a blue belt is 22.5 items/s, which is also 75% of 30 items/s, and obviously 22.5 items/s out can be fulfilled by a full red belt coming in.
Yellow is slightly trickier:
- Start calculating at the middle blue splitter, and assume that's the only bottleneck. (Starting from the input is left as an exercise for the reader; the exact same calculation works either way.)
- One lane of a blue splitter is 22.5 items/s.
- Half of that goes to the red belt, so 11.25 items/s.
- Conveniently, 11.25 happens to be exactly 75% of 15 items/s.
- The other 11.25 items/s loops back around and joins the input, and 11.25 items/s + 15 items/s is more than 22.5 items/s, so the input is large enough to completely refill the lane.
Blueprints:
Red belt:
Yellow belt: