think about this conceptually first. The difference between their rates of work is going to be the total speed at which the chalk board fills up (speed of writing - speed of erasing).
Ok, so we need to find the speed that Bart is writing, and the speed at which Nelson is erasing.
Bart: 50 minutes/ 1 board
However, we want to find his speed, which will be in boards/minute. Flip the fraction to get 1 board/50 minutes. Then multiply top and bottom by 1/50 in order to get 1/50 board per minute.
Bart's Speed = 1/50 board per minute
Do the same for Nelson, to get 1/80 board per minute (erasing).
The difference between these will be 1/50 - 1/80 = 3/400 board per minute
Since we want to know how long it will take to fill the board at this rate, we multiply 1 board * 1/(3/400) minute per board - this is the same as 1 * 400/3
So, the answer is 400/3 minutes, or 133.33 minutes, or 2 hours, 13 minutes.
#2
This is the same idea as #1. His speed without the headwind is 2000 miles/5 hours = 400miles/hour.
His speed with the headwind is 2000 miles/8 hours = 250 miles/hour.
400m/h - 250m/h = 150m/h
The speed of the wind is 150 miles/hour.