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At his usual rowing rate, Rahul can travel $12$ miles downstream in a certain river in six hours less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this $24$ miles round trip, the downstream $12$ miles would then take only one hour less than the upstream $12$ miles. What is the speed of the current in miles per hour?

- $\frac{7}{3}$
- $\frac{4}{3}$
- $\frac{5}{3}$
- $\frac{8}{3}$