# The odd theoretical ant

**Algebra**Level 5

The distance of \(P\) from the ant's starting point is \(kx\) meters, where \(k\) is a positive constant which can be expressed in the form \( \frac{a \sqrt {b}}{c} \), where \( \gcd(a,c) = 1\) and \(b\) is square free. Determine the value of \( a + b + c \).

**Challenge**: Determine an explicit formula for \(k\).