For minimizing, prove by exchange: If in the current pairing, a faster red is paired with a slower blue while a slower red is paired with a faster blue, swap them.
Let red[i] > red[j] and blue[i] < blue[j], with pairing (red[i], blue[i]) and (red[j], blue[j]). Speeds: max(red[i], blue[i]) + max(red[j], blue[j]). After swap (red[i], blue[j]) and (red[j], blue[i]): Speeds: max(red[i], blue[j]) + max(red[j], blue[i]). The swap never increases total speed. So sorted pairing is optimal.