When Desmond does 10 push-ups and 13 sit-ups, it takes a total of 56 seconds. In comparison, he needs 50 seconds to do 8 push-ups and 13 sit-ups. How long does it take Desmond to do each kind of exercise?
Let the time taken by Desmond to do 1 push-up be x seconds and the time taken by Desmond to do 1 sit-up be y seconds.
From the given information, we can set up the following equations:
10x + 13y = 56
8x + 13y = 50
Subtracting the second equation from the first equation, we get: 10x + 13y - (8x + 13y) = 56 - 50
Simplifying the equation, we get: 2x = 6
Dividing both sides of the equation by 2, we get: x = 3
Substituting the value of x in the first equation, we get:
10(3) + 13y = 56
Simplifying the equation, we get: 30 + 13y = 56
Subtracting 30 from both sides of the equation, we get: 13y = 26
Dividing both sides of the equation by 13, we get: y = 2
Therefore, Desmond takes 3 seconds to do each push-up and 2 seconds to do each sit-up. Answer: \boxed{3, 2}.