Final answer:
Samuel Slater solved the problem of competition in his textile mills by innovating with the Rhode Island system of labor and securing a tariff in 1816 to protect against British imports. This led to the success and expansion of the American textile industry in the early 19th century.
Step-by-step explanation:
Samuel Slater faced the challenge of protecting his textile mills from British competition. As an early industrial innovator in the United States, he had established the first successful water-powered cotton mill in Pawtucket, Rhode Island, based on designs he memorized before leaving Britain.
Slater employed the 'Rhode Island system' where entire families were hired and the father would oversee his family's labor, receiving credit instead of cash, which could be redeemed for rent or goods. This system and technological advancements allowed Slater's mills to thrive despite the competition.
To further protect his mills and the emerging American textile industry, Lobbyist Francis Cabot Lowell would successfully push Washington for a tariff in 1816, making imported English cotton fabric more expensive and giving American-made products a competitive edge.
Moreover, Slater's mills, which used water power and not yet steam engines, contributed significantly to the industrial growth in New England and inspired an increase in domestic manufacturing, especially with Jefferson's embargo of British products during 1807-1809.