Answer
It takes the lighter skater 13.3 seconds to reach the edge.
Work Step by Step
We can find the speed of the heavier skater after they push off.
$v = \frac{distance}{time}$
$v = \frac{30~m}{20~s}$
$v = 1.5~m/s$
After the two skaters push off, they will have the same magnitude of momentum. We can find the speed $v_L$ of the lighter skater.
$(50~kg)~v_L = (75~kg)(1.5~m/s)$
$v_L = \frac{(75~kg)(1.5~m/s)}{50~kg}$
$v_L = 2.25~m/s$
We can find the time it takes the lighter skater to travel 30 meters.
$t = \frac{distance}{speed}$
$t = \frac{30~m}{2.25~m/s}$
$t = 13.3~s$
It takes the lighter skater 13.3 seconds to reach the edge.
