There are two spaceships, A and B, moving towards each other, such that they will eventually pass each other. At a point equidistant from both ships, their velocities are both 0.5c towards that point.
Using relativistic velocity addition, the velocity of B in the reference frame of A is (1/(1.25))c, and vice versa. In the reference frame of A, a clock on B will be ticking slower than a clock on A, due to time dilation. Likewise, in the reference frame of B, a clock on A will be ticking slower than a clock on B, due to time dilation.
At the point at which they pass each other, the pilots of the ships show their clocks to each other via windows on their respective ships. My question is, will each pilot read both clocks differently from the other pilot? Pilot A should observe that his clock has been moving faster than Pilot B's, while Pilot B should observe that his clock has been moving faster than Pilot A's. Is there a paradox here, or have I been careless about something? (Note that I have been careful to avoid any acceleration/deceleration in this problem.)