A father three times as old as his son

Question

A father is currently three times as old as his son. In twelve years he will be only twice as old as his son. How old are they now? Then find a general rule: if the father is k times as old now and m times as old in t years, what is the son's age?

Accepted Answer

The son is 12 and the father is 36. Using the age gap. Let the son be s years old. The father is 3s, so the gap is 2s. In twelve years the son is s + 12 and the father is 2(s + 12), so the gap is s + 12. The gap is constant: 2s = s + 12, giving s = 12 and the father 36. Check. In twelve years: son 24, father 48, and 48 is twice 24. The general rule. Now: father = ks, gap = (k minus 1)s. In t years: father = m(s + t), gap = (m minus 1)(s + t). Equate: (k minus 1)s = (m minus 1)(s + t), so s = (m minus 1)t / (k minus m). With k = 3, m = 2, t = 12: s = 12/1 = 12. The formula also warns you when …

A father three times as old as his son

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