We study the spreading of viruses, such as SARS-CoV-2, by airborne aerosols, via a first-passage-time problem for Lagrangian tracers that are advected by a turbulent flow: By direct numerical simulations of the three-dimensional (3D) incompressible Navier-Stokes equation, we obtain the time tR at which a tracer, initially at the origin of a sphere of radius R, crosses the surface of the sphere for the first time. We obtain the probability distribution function P(R,tR) and show that it displays two qualitatively different behaviors: (a) for R≪LI, P(R,tR) has a power-law tail ∼t−αR, with the exponent α=4 and LI the integral scale of the turbulent flow; (b) for LI≲R, the tail of P(R,tR) decays exponentially. We develop models that allow us to obtain these asymptotic behaviors analytically. We show how to use P(R,tR) to develop social-distancing guidelines for the mitigation of the spreading of airborne aerosols with viruses such as SARS-CoV-2.