Explain the segment of decant theorem for geometry

Segments from Secant and Tangents. If a tangent and secant meet at a common point outside the circle, the segments created have a similar relationship to that of two secant rays.

Assuming he's going 12 miles per hour, and 10 miles per hour.

Firstly he rode his bike for 2 1/3 hours at 12 miles per hour, 
12 miles = 1 hour
24 miles = 2 hours
4 miles = 1/3 hour

He rode 28 miles in the first 2 1/3 hours.

Secondly, he rode his bike at the speed of 10 miles per hour for 1 1/2 hours
10 miles = 1 hour
5 miles = 1/2 hour

He rode his bike for 15 miles for the next 1 1/2 hours, together he rode his bike for 43 miles (28 + 15).