#### Answer

The space traveler will weigh $405N$ on that planet.

#### Work Step by Step

Take the mass of the traveler to be $m$. For Earth's mass $M$, Earth's radius $r$ and gravitation constant $G$, the weight of the traveler is
$$W_E=G\frac{mM}{r^2}=540N$$
On another planet with mass $3M$ and radius $2r$, the weight of the traveler is $$W_P=G\frac{m3M}{(2r)^2}=\frac{3}{4}G\frac{mM}{r^2}=\frac{3}{4}W_E$$ $$W_P=405N$$