Answer :
Final answer:
To find out how long it will take for Bart and Nelson to cover the whole board while working simultaneously, we need to determine their combined rate of work. By adding their individual work rates, we can calculate the time it will take them to finish the task.
Explanation:
To find out how long it will take for Bart and Nelson to cover the whole board while working simultaneously, we need to determine their combined rate of work. Bart takes 50 minutes to cover the whole board, so his work rate is 1/50 of the board per minute. Similarly, Nelson takes 80 minutes to erase the board, so his work rate is 1/80 of the board per minute.
When they work together, their work rates add up. So their combined work rate is 1/50 + 1/80 = 3/160 of the board per minute.
To find out how long it will take them to cover the whole board, we can use the formula:
Time taken = 1 / Combined work rate
Plugging in the values, we get:
Time taken = 1 / (3/160) = 160/3 minutes, which is approximately 53.33 minutes.
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.
