How and why did railroad
companies convince farmers
to purchase land in West
Texas?

To increase the value of the land.

Explanation:

Existence of Agricultural businesses in  a certain territory tend be followed by an influx of migration toward that territory since Agricultures provide the basic needs that humans need to live. As more populations arrive in that area, the value of the land will increase.

Railroad companies convinced farmers to purchase it by promising that they will built their rails there in order to make it easy for the farmers to distribute their products. If the population in that area increased, the railroad companies will also be benefited since increased population will provide them with more customers.

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