How did columbus search for a western route to china pave the way for other countries to explore the americas

Now, other countries, such as Portugal, Spain, and, later on, England had a rough idea of what was West of Europe. Columbus helped show how long it took to get there, so they would know how much food to pack for the voyage. They also now had an idea of the people who lived there, even though they didn't treat the Natives of Hispaniola and Americas like people. 
Hope this helps! Please let me know if I'm wrong :)