Iron emits a K_α X-ray with an energy of 6.4 keV , while calcium...

Both iron $K_\alpha$ and calcium $K_\alpha$ are X-ray photons, which are electromagnetic waves.

All electromagnetic waves travel at the speed of light in vacuum or air, which is $c = 3 \times 10^8 \text{ m/s}$, irrespective of their energy or wavelength.

The distance to be traversed is $d = 3 \text{ km} = 3 \times 10^3 \text{ m}$.

The time taken by both photons is given by $t = \dfrac{d}{c}$.

$t = \dfrac{3 \times 10^3}{3 \times 10^8} = 10^{-5} \text{ s} = 10 \mu\text{s}$.

Thus, both photons take $10 \mu\text{s}$ to traverse the distance.