Superposition and average power dissipation
It is an exercise to force you to think about the properties of linear systems.

What you know about that box lets you conclude that the overall system is linear (box+generators+load). Therefore you can apply superimposition to compute the voltage across the load.

The voltage across the load will be the superimposition of two sinusoidal components at different frequencies. You don't need to know which phase and which amplitude they have (the amplitude will depend on the transfer function of the box, which is unknown, but not frequency-dependant). The transfer function is therefore a simple constant (less than 1, since the box is passive). Let's call it \$\alpha_1\$ and \$\alpha_2\$.

Since there are no reactive elements in the box, there will be no phase difference between the stimuly and the respective response across the load.

In the end, you can deduce that the voltage across the load has the following form:

$$
v_{load}(t) = \alpha_1 A \sin(\omega_1 t ) + \alpha_2 A \sin( \omega_2 t + \theta)
$$

From this point on you can proceed by yourself. Apply the definition of average power to that expression and to the average power at the input and see what you get and what you can conclude.