In a storage room, a heavy box of mass $10.0$ kg is initially at rest on a spring with a spring constant of $800$ N/m. The box is part of a pulley system where it is connected to a $3.0$-kg package. When the system is released, the heavier box compresses the spring by moving downwards, pulling the lighter package upwards. Calculate the distance the box falls, compressing the spring, before the entire system momentarily comes to rest.