Decoding Family Ages: A Mathematical Puzzle

When exploring the intricacies of family relationships and the passage of time, a fascinating puzzle can arise. This particular puzzle involves understanding the ages of family members at different points in time, using a mathematical framework. Let's delve into the details of this intriguing problem and unravel the solution.

Imagine a scenario where, when the mother was 28 and the father was 30, the child was exactly 2 years old. Given that the child is now 10 years old, the question is, how old are the mother and father now?

Understanding the Initial Conditions

The problem states that when the child was 1/14th the age of the mother and 1/15th the age of the father, it was 2 years old. Therefore, we can determine the following:

The child was 2 years old. The mother was 28 years old. The father was 30 years old.

From these initial conditions, we can begin to build a timeline of the passage of time.

Calculating the Time Elapsed

Since the child is now 10 years old, we need to determine how many years have passed since the child was 2 years old. It can be calculated as follows:

Child's age now: 10 years Age of child at initial condition: 2 years Time elapsed: 10 - 2 8 years

This 8-year period is crucial in determining the current ages of the mother and father.

Current Ages of the Parents

Given that 8 years have passed, we can add this period to their ages at the initial condition:

Initial age of mother: 28 years Initial age of father: 30 years Time elapsed: 8 years Current age of mother: 28 8 36 years Current age of father: 30 8 38 years

Therefore, the current ages are as follows:

Mother: 36 years old Father: 38 years old

This solution is derived by following a logical sequence of events and applying basic arithmetic to account for the passage of time.

Conclusion

By carefully examining the ages at a specific point in time and the subsequent passage of years, we can accurately determine the current ages of the parents. This puzzle not only highlights the importance of logical reasoning but also demonstrates the mathematical approach to solving age-related problems.