S = [k1 /(x^2)] +[k2 / (20 -x)^2] ----(i)

Since k1 = 27k2,

S = [27k2 /(x^2)] +[k2 / (20 -x)^2] ----(ii)

To find the minimum S, we equate dS/dx to zero.

Remember, k1 and k2 are constants.

Differentiate both sides of (ii) with respect to x,

dS/dx = (27k2)[-2 /(x^3)] +(k2)[(-2 / (20 -x)^3) * (-1)]

dS/dx = [-54k2 /(x^3)] +[2k2 / (20 -x)^3]

Set that to zero,

0 = [-54k2 /(x^3)] +[2k2 / (20 -x)^3]

0 = (-54k2)(20 -x)^3 +(2k2)(x^3)

0 = -54(20 -x)^3 +2x^3

0 = -27(20 -x)^3 +x^3

27(20 -x)^3 = x^3

Get the cuberoots of both sides,

3(20 -x) = x

60 -3x = x

60 = x +3x

x = 60/4 = 15 miles