How did western imperialism spread through Africa and Asia so quickly ?

There were several reasons why western imperialism spread so quickly through Africa and Asia. The European countries were constantly looking for more land to conquer. These countries were in a race to see which country could get control of the most land, obtain valuable resources, and establish military bases.
Once the Industrial Revolution began, the need for these resources increased. It was cheaper to get resources from a colony than to buy them from other countries. Plus, these countries needed a place to sell the products they made. Establishing colonies in Africa and in Asia would help them accomplish these goals.
The different groups of people living in Africa and in Asia were no match for the powerful militaries of the European powers. When the Europeans moved into an area, they were often able to conquer the land without too much difficulty.
Finally, many of the European powers saw it as their duty to spread their way of life to people who they believed were inferior to them. They also saw an opportunity to spread their religion and convert people to it. The European powers wanted to do these things as soon as possible.
http://webs.bcp.org/sites/vcleary/ModernWorldHistoryTextbook/Imperialism/section_2/motives.html