Calculus in Games

Max is a virtual character in a particular 2D game. He has the choice of $2$ functions (curve) to walk on to collect coins.

• Road 1 $\frac{x^3}{6} + \frac{1}{4x}$ from $0 \leq x \leq 5$ where there are $20$ coins evenly distributed along this arc.
• Road 2 $\ln {(\sec {x}})$ from $0 \leq x \leq \frac{\pi}{3}$ where there is $1$ coin along this arc.

Which function is the most coin-to-distance efficient for him to take? (Meaning which function should he walk to gain more coin in a unit distance?)