Alice can solve x sudoku puzzles in 4 hours and Betty can Y sudoku puzzles in 5 hours. Both of them can solve (3y-x-1) Sudoku puzzles in 3 hours. Alice and Betty can solve 7 sudoku puzzles in 1 hour. Find the difference in the number of Sudoku Puzzles at which Alice and Betty can solve in 1 hour.

Answer 1

First, let's find the number of Sudoku puzzles Alice can solve in 1 hour. Alice can solve x puzzles in 4 hours, so in 1 hour she can solve x/4 puzzles.
Similarly, Betty can solve y puzzles in 5 hours, so in 1 hour she can solve y/5 puzzles.
We are told that (3y-x-1) puzzles can be solved by Alice and Betty together in 3 hours. Therefore, in 1 hour they can solve (3y-x-1)/3 puzzles.
The total number of puzzles they can solve together in 1 hour is 7.
So, x/4 + y/5 = 7.
Multiplying through by 20 (to eliminate the fractions) gives 5x + 4y = 140.
Now we can see the difference between the number of puzzles Alice and Betty can solve by comparing the coefficients of x and y.
For Alice, the coefficient is 5, and for Betty, the coefficient is 4.
Thus, the difference in the number of Sudoku puzzles that Alice and Betty can solve in 1 hour is 5 - 4 = <<5-4=1>>1. Answer: \boxed{1}.