Call the power of the weaker source P and the stronger 3P. I'm putting the weaker source on the origin and the stronger one at x = 10 ft. Put the object at x = d. The total intensity at this point is:

Now find the minimum of I with respect to the position d. (ie. Take the derivative of I with respect to d, set it equal to 0, and solve for d. Then you need to show that this value of d is, in fact, a minimum point rather than a maximum.)

Warning: You are going to have to solve an ugly cubic equation. Don't even bother trying to factor it: I'd recommend a numerical solution. For reference, I'm getting d around 4.09 ft.

-Dan