# Problem of the Week Problem C Two Paths

Points $$R$$, $$S$$, $$T$$, $$U$$, $$V$$, and $$W$$ lie in a straight line. There are two curved paths from $$R$$ to $$W$$. The upper path is a semi-circle with diameter $$RW$$. The lower path is made up of five semi-circles with diameters $$RS$$, $$ST$$, $$TU$$, $$UV$$, and $$VW$$.

It is also known that the distance from $$R$$ to $$W$$ in a straight line is $$1000~$$m, and $$RS=ST=TU=UV=VW$$.

Starting at the same time, John and Betty ride their bicycles along these paths from $$R$$ to $$W$$. Betty follows the upper path and John follows the lower path. If they bike at the same speed, who will arrive at $$W$$ first?

Theme: Geometry