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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?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.