Five friends live on the same street. Their houses are at points $A,$ $B,$ $C,$ $D,$ and $E,$ with the distances shown. [asy] unitsize(1 cm); pair A, B, C, D, E; A = (0,0); B = (1,0); C = (2,0); D = (5,0); E = (7,0); draw(A--E); dot("$A$", A, S); dot("$B$", B, S); dot("$C$", C, S); dot("$D$", D, S); dot("$E$", E, S); label("$1$", (A + B)/2, N); label("$1$", (B + C)/2, N); label("$3$", (C + D)/2, N); label("$2$", (D + E)/2, N); [/asy] The five friends decide to meet at point $P$ so that the total walking distance for all five friends is minimized. What is $AP?$

if the latex doesn't work then...

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

AB = 1, BC = 1, CD = 3, DE = 2 (On the same line)

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

Guest Feb 11, 2022