A bicyclist starts his ride home from a point 10 miles away from his house going 5 miles per hour (assume the road is a perfect straight line). At the same time, a bee, initially sitting on his helmet (always wear your helmet!), takes off and flies toward the house at the speed of 15 miles per hour.

Upon reaching the house, the bee turns right around and flies back toward the bicyclist. When it reaches him it turns around again and flies back to the house. The bee keeps doing this until the man finally arrives at the house himself.

What total distance did the bee cover by that point in time?