Adam Clarke on John 11:20

Martha - went and met him - Some suppose she was the eldest of the two sisters - she seems to have had the management of the house. See Luk 10:40.

Mary sat still in the house - It is likely that by this circumstance the evangelist intended to convey the idea of her sorrow and distress; because anciently afflicted persons were accustomed to put themselves in this posture, as expressive of their distress; their grief having rendered them as it were immovable. See Ezr 9:3, Ezr 9:4; Neh 1:4; Psa 137:1; Isa 47:1; Luk 1:79; and Mat 27:61.