Problem 40 Solution

Let y be the solution. Let x=4-y. The time to reach the finish line is:

t=(4-x)/6 + (1+x²)^1/2/2.

Set the derivative equal to 0:

dt/dx= -1/6 + 1/2 * 1/2 * 2x * (1+x²)^-1/2 = 0.

The solution is x=1/8^1/2.

y=4-x.

Michael Shackleford, A.S.A.