+0  
 
0
263
1
avatar

Five friends live on the same street. Their houses are at points A, B, C, D, and E, with the distances shown.

 

 

 

The five friends decide to meet at point P so that the total walking distance for all five friends is minimized. What is AP?

 Sep 26, 2021
 #1
avatar
0

 

If everybody meets at 

A, the total distance walked by A is 0, by B is 5, by C is 9, by D is 11, by E is 14, total 39  

B, the total distance walked by A is 5, by B is 0, by C is 4, by D is 6, by E is 9, total 24  

C, the total distance walked by A is 9, by B is 4, by C is 0, by D is 2, by E is 5, total 20  

D, the total distance walked by A is 11, by B is 6, by C is 2, by D is 0, by E is 3, total 22  

E, the total distance walked by A is 14, by B is 9, by C is 5, by D is 3, by E is 0, total 31 

 

Let's try to improve on the 20 total  

 

If everybody meets halfway between  

B and C, the total distance walked by A is 7, by B is 2, by C is 2, by D is 4, by E is 7, total 22  

C and D, the total distance walked by A is 10, by B is 5, by C is 1, by D is 1, by E is 4, total 21  

 

It appears that if you move left of C, the total distance increases, 

and likewise, if you move right of C, the total distance increases.  

 

I don't know if this is the right way to find the answer, but I'd put my money on P is at the home of C  

Therefore A to P is 9      I'm not going to highlight this in red because I'm not relatively confident.  

.

 Sep 26, 2021

3 Online Users

avatar
avatar
avatar