The rules for a race require that all runners start at $A$, touch any part of the 1200-meter wall, and stop at $B$. What is the number of meters in the minimum distance a participant must run? Express your answer to the nearest meter.

michaelcai  Oct 24, 2017

Let the place that they touch be x meters from the 300 m wall

Then the distance from the 500 m wall will be 1200 - x


Then....the total distance, D, can be expressed as


D = sqrt [ x^2 + 300^2 ] + sqrt [ (1200 - x)^2 + 500^2 ]


This can be solved with Calculus, but it's a little messy


A graph seems better : 




The graph shows that the minimum distance is achieved when x = 450m

And the minimum distance  ≈  1442 m


By the way......we can show that this is true if


arctan [ 300 / 450]   =  arctan [ 500 / 750 ]  ......and this is true  !!!!



cool cool cool

CPhill  Oct 24, 2017

3 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.