Crossing the Desert

The explorer Sir Randolph Fiend set out to cross the Little Red Desert alone on foot. The length of the crossing is 150 km and Fiend could cover 30 km a day. Food and water were available on the other side but he could carry no more than three days' rations. Nevertheless, after some careful planning Fiend managed to make the crossing - in the shortest time possible in the circumstances. How long did he take?

The answer is supposed to be 11.8 days and I have a worked solution by a maths professor from James Cook University and I still can't see it! And even he couldn't prove this answer is a minimum!

Good Luck!

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