The difference stays the same

A father is 4 times as old as his son. In 12 years' time, he will be twice as old as his son. How old is the son now? Try it first. Pause if you like. Before we draw, notice one thing. Both of them get the same 12 years, so the difference between their ages never changes. Watch. Call the son's age 1 unit. Then the father is 4 units. And the age difference between them is 3 blue units. Now add the 12 years. Both of them get 12 years older, so both bars grow by the same purple stretch. They both got older by the same 12 years, so the age difference never changes. It's still 3 blue units. In 12 years' time, the father is twice as old. So later, the father is 2 new blocks, and the son is 1 new block. Now look at the age difference. It's exactly one of the father's blocks. Remember the age difference between them never changes, so it is the 3 blue units. And later, that same age difference is 1 new block. So 1 new block is 3 blue units. Now looking at the son's later age, it's 1 blue unit plus the purple 12 years. We know that this is also 1 new block, which is also 3 blue units. Both rows are the same age, and both start with 1 blue unit. So the purple 12 covers exactly 2 blue units. 2 units is 12. So 1 unit is 6 years. The son's age now is 1 unit. The son is 6 years old now. Check it. At 4 units, the father is 24 years old now. In 12 years' time, the father will be 36 years old and the son will be 18 years old, so the father is twice as old as the son. When both change by the same amount, the difference between them stays the same.