Question

why were farmers dependent on banks and railroads in the late 19th century?

Answer 1

This article gives an explanation of that.

http://encarta.msn.com/text_1741500823___104/United_States_History.html

Answer 2

Farmers had to borrow money to buy and run the farm (buy seed, plow, etc.) during the year. The farmer only made money to pay the bank back when the harvest was in and sold (if in the mid west, probably shipped over the railroad).
Farmers needed to get their crops to the markets. Customers lived in the cities and many of the farms were out on the plains. There was no interstate highway system with trucks rolling to market. The canals helped; for example the Erie Canal helped a lot, but away from the rivers and canals, the farm was only practical near the railroad track.