The US economy borrowed heavily from the British in the nineteenth century to build a railroad system. Why (and how) did this make both countries better off?

Because of the law of diminishing returns

Explanation:

as the Brithish were industrialized but, the US don't adding capital int oUS was more profitable than adding into the British territory.

This expanded to all English colonies and other countries besides the commonwealth.

The goal for the victorian businessman was to incrase their wealth thus, they looked for opportunities in the world market being those, in Africa, South America, the Asian southern and the US. The railroad was along the textile one of the most profitable as it was the only alternative to move on horseback from one city into another. Being as large as the US, once the Brithish ended theirs, they invest in other countries to make gain.