Faster/slower

A person moves from a point $(-1,1)$ to $(1,-1)$.

  • While moving above the $x$ axis their rate is $k_1$

  • Whilen moving below their rate is $k_2$.

What crossing point $x$ in $[-1,1]$ minimizes time?

$k_1 =$ 1.0

$k_2 =$ 1.0

$x =$ 0.0