Comparative Ages — “Joan is 42, Kelvin is 26. How many years ago was Kelvin exactly half of Joan?”

Introduction / Context:We look for a past time t such that Kelvin’s age then equals half of Joan’s age then. Set up a linear equation in t and solve; it is straightforward proportional reasoning with a time shift.

Given Data / Assumptions:

• Joan now = 42, Kelvin now = 26.
• t years ago: Kelvin 26 − t; Joan 42 − t.
• Target: 26 − t = (42 − t)/2.

Concept / Approach:Clear the fraction by multiplying both sides by 2, then isolate t. Ensure t is positive and realistic.

Step-by-Step Solution:

Verification / Alternative check:10 years ago: Kelvin 16; Joan 32; indeed 16 is half of 32.

Why Other Options Are Wrong:6/4/8/12 do not satisfy the equality when substituted for t.

Common Pitfalls:Setting 26 = 42/2 without the time shift; or subtracting t from only one person’s age.

Final Answer:10 Years