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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 \(VW\).

The lower path is a winding path that travels from R to W passing through S, T, U and then V along the way.

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