Final answer:
Mrs Archer and Janey nearly set a record of only speaking with hotel and railway station employees during their European travels.
Step-by-step explanation:
The record that Mrs Archer and Janey almost achieved was exchanging words only with hotel and railway station employees while visiting Europe. Despite being in foreign countries, they almost exclusively communicated with individuals serving them in hotels or at railway stations, which indicates a significant degree of separation from the local populations and a missed opportunity to engage more deeply with foreign cultures. The record that Mrs. Archer and Janey almost achieved is never speaking to a foreigner other than those employed in hotels and railway stations.