Answer
Carmelita's mass is $~~57.6~kg$
Work Step by Step
In the initial position, the center of mass is closer to Ricardo than Carmelita because Ricardo is heavier.
In the final position, the center of mass is closer to Ricardo than Carmelita because Ricardo is heavier.
Note that the position of the center of mass does not move as the canoe moves 40 cm horizontally.
By symmetry, the center of mass must be located 20 cm from the center of the canoe in the initial and final positions.
Let $M$ be Carmelita's mass and let Carmelita's initial position be $x=0$.
Then Ricardo's initial position is $x=3.0~m$ and the empty canoe's initial position is $x=1.5~m$
The initial position of the center of mass must be $x=1.7~m$
We can find $M$:
$x_{com} = \frac{(M)(0)+(30)(1.5)+(80)(3.0)}{M+30+80} = 1.7$
$(30)(1.5)+(80)(3.0) = (1.7)(M+110)$
$45+240 = 1.7~M+187$
$M = \frac{98}{1.7}$
$M = 57.6~kg$
Carmelita's mass is $~~57.6~kg$
