Answer:
To find the difference in the number of Sudoku puzzles that Alice and Betty can solve in 1 hour, we need to compare their individual rates of puzzle-solving.
Let's start by finding the rates at which Alice and Betty can solve Sudoku puzzles:
Alice can solve x Sudoku puzzles in 4 hours, so her rate of solving is x puzzles per 4 hours, which can be simplified to (x/4) puzzles per hour.
Betty can solve y Sudoku puzzles in 5 hours, so her rate of solving is y puzzles per 5 hours, which can be simplified to (y/5) puzzles per hour.
Now, let's use the given information that both Alice and Betty can solve (3y-x-1) Sudoku puzzles in 3 hours.
We can set up the equation:
(3y-x-1) puzzles / 3 hours = 7 puzzles / 1 hour
Simplifying the equation:
(3y-x-1) / 3 = 7
Multiplying both sides by 3:
3y-x-1 = 7 * 3
Simplifying:
3y-x-1 = 21
Now, let's solve for x:
x = 3y - 22
Now that we have the relationship between x and y, we can find the rates of puzzle-solving for Alice and Betty:
Alice's rate: (x/4) puzzles per hour
Betty's rate: (y/5) puzzles per hour
To find the difference in the number of Sudoku puzzles they can solve in 1 hour, we subtract Betty's rate from Alice's rate:
Difference = Alice's rate - Betty's rate
Difference = (x/4) - (y/5)
Substituting the value of x:
Difference = ((3y - 22)/4) - (y/5)
Now, let's simplify the equation:
Difference = (15(3y - 22)/60) - (12y/60)
Difference = (45y - 330)/60 - (12y/60)
Difference = (45y - 330 - 12y)/60
Difference = (33y - 330)/60
Therefore, the difference in the number of Sudoku puzzles that Alice and Betty can solve in 1 hour is (33y - 330)/60.