Don't get stuck on the translation "meanwhile". That is only an approximation. A literal translation would be "and in this" meaning something like:
"while this is going on" (here, work in the field)"while these things are happening"Mother μὲν is preparing supper,
daughter δὲ is setting the tableson δὲ is strumming his guitarἐν δὲ τοῦτῳ the bell rings. It's the police. Why?
I'm up a ladder, paint pot and brush in hand, painting away furiously.
ἐν δὲ τούτῳ the phone rings.....
The little boys are playing cowboys and Indians.
ἐν δὲ τούτῳ it gets dark but they are so engrossed in their game that they do not notice and go on playing
ἐν δὲ τούτῳ their waiting mothers are becoming more and more worried
A young man is waiting for his girl-friend in front of the cinema. She's late again.
ἐν δὲ τούτῳ a taxi draws up and out steps a most gorgeous woman. The young man can't help but stare at her in admiration.
ἐν δὲ τούτῳ his girl friend turns up and sees him staring. Oh dear!