Final answer:
To find the two consecutive positive integers, set up an equation using the information given. Solve the equation to find the value of the first integer and its consecutive positive integer.
Step-by-step explanation:
To find the two consecutive positive integers, we can set up an equation using the information given. Let's assume the first positive integer is x. The second consecutive positive integer would then be x + 1. We know that the difference between the reciprocals of these two numbers is 1/12. So, we can set up the equation:
1/x - 1/(x + 1) = 1/12
To solve this equation, we can multiply both sides by a common denominator of 12x(x + 1). This gives us:
12(x + 1) - 12x = x(x + 1)
Simplifying further:
12x + 12 - 12x = x^2 + x
12 = x^2 + x
This is a quadratic equation. We can rearrange it and solve by factoring or by using the quadratic formula. Once we find the value of x, we can determine the two consecutive positive integers by adding 1 to x.