Time does play a part in the operation, but it is not necessary to get all wrapped up in a race against the clock. Panic is definitely not good for your brushwork. Let's consider what can be done to take the edge off the process.
The option that may come to mind first is to PAINT FASTER! This is not terrifically helpful, since efficiency comes from long term experience, and we are looking for what can be adopted today. Instead of speeding ourselves up, then, how about slowing down the drying time?
That hillside in the background of the photo comprises 4 or 5 different applications of paint. Starting with the lightest layer, a "common denominator" of very pale, warm neutral can be applied to the whole shape (leaving the foreground trees white). Now, while that first wash is still wet, the middle value areas - the forest green and the rock shadows - can be painted. These are followed by the darker green shadows and the darkest recesses within the rock shapes.
That's a lot of color mixing and brushwork. Chances are the initial wash could be dry before you even finished the middle values.
You make that wash wetter. A lot wetter. Then, when you prepare the brush for the additions just make sure it's drier than the paper, to prevent blooms.
Of course, the wash will eventually dry, no matter how wet you make it, so watch for hard edges you don't want. If you see one, stop painting and dry the paper thoroughly. Now you can re-wet it and proceed making soft edges.
Back to the photo. Notice that the foreground lights are lighter than those in the background and the darks are darker. This difference in the value range contributes to the feeling of space. Using hard edges in the foreground would add to the illusion.
For homework, look for an image with areas that have multiple layers with soft edges, or use the one you brought home from class. Practice the complex parts on good quality paper. When you feel confident, try putting it all together in a proper painting.