Asking a Jew to help a goy on Shabbat

Is it permissible for an observant Jew to ask his Jewish Shabbat guest to help the non-Jewish maid? Specifically, the non-Jew is washing the dishes on Shabbat morning and the Jewish guest is told to dry the dishes with a terrycloth towel ("She will be washing, you will be drying"). (This has actually happened).

There is no problem to help the non-Jewish maid as long as no relationships develop. Rabbi Binyamin Bamberger