The difference between two positive integers is 36. The quotient when one integer is divided by another is 4. Find the integers.

Let's denote the two positive integers as x and y. We are given two pieces of information:

The difference between the two integers is 36: x - y = 36.
The quotient when one integer is divided by the other is 4: x / y = 4.
From the second equation, we can rewrite it as x = 4y and substitute this expression into the first equation:

4y - y = 36

Simplifying the equation, we have:

3y = 36

Dividing both sides of the equation by 3, we find:

y = 12

Now we can substitute the value of y back into the equation x = 4y:

x = 4 * 12 = 48

Therefore, the two positive integers are 48 and 12.