Relative

A problem from the October 1962 issue of Eureka, the journal of the Cambridge University Mathematical Society:

Tom is twice as old as Dick was when Tom was half as old as Dick will be when Tom is twice as old as Dick was when Tom was a year younger than Dick is now. Dick is twice as old as Tom was when Dick was half as old as Tom was when Dick was half as old as Tom was two years ago. How old are Dick and Tom?

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