Context : An important aspect of quenching star formation is the removal of the cold interstellar medium ( ISM ; non-ionised gas and dust ) from a galaxy .
In addition , dust grains can be destroyed in a hot or turbulent medium .
The adopted timescale of dust removal usually relies on uncertain theoretical estimates .
It is tricky to track dust removal because the dust is constantly being replenished by consecutive generations of stars .

Aims : Our objective is to carry out an observational measurement of the timescale of dust removal .

Methods : We explored an approach to select galaxies that demonstrate detectable amounts of dust and cold ISM coupled with a low current dust production rate .
Any decrease of the dust and gas content as a function of the age of such galaxies must , therefore , be attributed to processes governing ISM removal .
We used a sample of the galaxies detected by Herschel in the far-infrared with visually assigned early-type morphology or spirals with red colours .
We also obtained JCMT/SCUBA-2 observations for five of these galaxies .

Results : We discovered an exponential decline of the dust-to-stellar mass ratio with age , which we interpret as an evolutionary trend for the dust removal of these galaxies .
For the first time , we have directly measured the dust removal timescale for such galaxies , with a result of \tau = ( 2.5 \pm 0.4 ) Gyr ( the corresponding half-life time is ( 1.75 \pm 0.25 ) Gyr ) .
This quantity may be applied to models in which it must be assumed a priori and can not be derived .

Conclusions : Any process which removes dust in these galaxies , such as dust grain destruction , can not happen on shorter timescales .
The timescale is comparable to the quenching timescales found in simulations for galaxies with similar stellar masses .
The dust is likely of internal , not external origin .
It was either formed in the past directly by supernovae ( SNe ) or from seeds produced by SNe , and with grain growth in the ISM contributing substantially to the dust mass accumulation .