Final answer:
To find out how many years later the product of their ages will be 420, we can set up an equation using variables for their ages. By solving the equation, we find that it will take approximately 10.5 years for the product of their ages to be 420.
Step-by-step explanation:
To solve this problem, let's assign variables to the ages of the man and his son. Let the man's age be represented by 'M' and the son's age be represented by 'S'. We are given that the man is 40 years old, so M = 40. We are also given that the son is 8 years old, so S = 8.
We need to find the number of years, represented by 'x', that pass until the product of their ages is 420. The product of their ages is given by M * S. So, M * S = 420.
We can set up the equation 40 * 8 = 420 and solve for x. Dividing both sides of the equation by 40 gives us 8 = 420 / 40. Simplifying further, we find that x = 420 / 40 = 10.5.
Therefore, it will take approximately 10.5 years for the product of their ages to be 420.