Dylan's Math Sets

Dylan is writing solutions to his problems for some math sets. There are \(25\) problems on his set, and while he is incredibly fast at solving problems, he is quite slow at writing up solutions. He takes \(x\) minutes to solve the \(xth\) problem, but to write it up, it takes him \(x^{2}\) minutes.

If it takes him \(6\) minutes to prepare his set (like writing his name, and the date etc.) and he plans to finish the set over \(3\) days, how much time should he spend on it each day? Express your answer as: if it takes him \(m\) hours and \(n\) minutes, your answer should be \(n + m\).

For example, the \(5th\) problem would take him \(5\) minutes to solve, but \(25\) (\(5^{2}\)) minutes to write it up. Assume that he does an equal part each day. Also assume that Dylan does not live on Earth; he lives on a planet with 100 hour days.

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