Walking in the Mountains
Heidi and Peter pass two signs which say how far their destination is. How long will it take them to get there?
Age
14 to 16
Challenge level
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.
Answer: 2 pm
12 noon: 2 hours 55 minutes = 175 minutes
1 o'clock: 1 hour 15 minutes = 75 minutes
They travel 100 sign-minutes in 1 hour
So they will travel the remaining 75 sign-minutes in $\frac34$ hour = 45 minutes
They set off after lunch at 1:15 and arrive 45 minutes later at 2.