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Heidi and Peter went for a mountain walk from Obersee to Salzbau. They left Obersee at 12 noon and the sign there said that Salzbau was $2$ hours and $55$ minutes away. At one o'clock they sat down for lunch under another sign which said that Salzbau was now only $1$ hour and $15$ minutes away. After stopping for $15$ minutes for lunch, they continued their walk at the same speed as before without any further breaks. At what time did they reach Salzbau?

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This problem is taken from the UKMT Mathematical Challenges.
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