Searching JRI-Poland with surname begins BAR and town phonetically like Plock turns up the following family in the book of residents:
Josek BARABEL & Ryfka Ruchla (nee KWIATEK), with children Pejsak Majer (born 1878), Jochejwet (born 1881) and Dawid Jakub (born 1886).
There is also the marriage record in 1877 and birth records for the three children and a fourth child: Abram Isaak, born in 1893.
Apart from the father's name being Josek/Josef instead of Benjamin, there is a good correlation with the family you are searching: Majer->Mark, Jakub->John and Abraham ->Adolph.
The book of residents gets you back another generation, because it gives the names of the parents of Josek & Ryfka Ruchla.
I hope this helps,