We use the eagle simulations to study the connection between the quenching timescale, τ Q , and the physical mechanisms that transform star-forming galaxies into passive galaxies. By quantifying τ Q in two complementary ways -as the time over which (i) galaxies traverse the green valley on the colour-mass diagram, or (ii) leave the main sequence of star formation and subsequently arrive on the passive cloud in specific star formation rate (SSFR)-mass space -we find that the τ Q distribution of high-mass centrals, low-mass centrals and satellites are divergent. In the low stellar mass regime where M < 10 9.6 M , centrals exhibit systematically longer quenching timescales than satellites (≈ 4 Gyr compared to ≈ 2 Gyr). Satellites with low stellar mass relative to their halo mass cause this disparity, with ram pressure stripping quenching these galaxies rapidly. Low mass centrals are quenched as a result of stellar feedback, associated with long τ Q 3 Gyr. At intermediate stellar masses where 10 9.7 M < M < 10 10.3 M , τ Q are the longest for both centrals and satellites, particularly for galaxies with higher gas fractions. At M 10 10.3 M , galaxy merger counts and black hole activity increase steeply for all galaxies. Quenching timescales for centrals and satellites decrease with stellar mass in this regime to τ Q 2 Gyr. In anticipation of new intermediate redshift observational galaxy surveys, we analyse the passive and star-forming fractions of galaxies across redshift, and find that the τ Q peak at intermediate stellar masses is responsible for a peak (inflection point) in the fraction of green valley central (satellite) galaxies at z ≈ 0.5 − 0.7.