Saturday, 11 June 2016

A Mathematician's Holiday - Problem 5: Hotel Fire!

Some pieces of string, or rope, depending on the size of your demonstration and a play to draw the diagram below in Figure 1. Note that it does not have to be too accurate.
Having got to the hotel we unfortunately find that it is on fire. Thankfully, there is a river very close to our location, where we can load up buckets with water and, thus, help put the fire out. What is the quickest route from our location, to the river and to the hotel?
Figure 1. Problem set up.

This problem is very similar to "Late for the Plane" and works well if they are done in combination with one another. Again, the question relies on using the ropes to measure distance, in order to measure time.

A critical point for the audience to understand is that the helpers all run at the same speed, even when they are carrying water.

Suppose we run slower once we are carrying water. How does this extra facet influence the solution?  Note that you can solve this problem as well, however, but it is far more involved and involves calculus.

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