I agree with Keith.
Similarly, in a tailwind, the max range will be achieved at a speed slightly slower than that for still air. We want to spend a little more time in the beneficial tailwind, so slowing down a bit helps overall.
For a jet, the max range speed is found on the 'drag v speed' graph. A straight line drawn from the origin which just touches the curve will have a minimum angle to the x-axis. The speed corresponding to this tangent (vertically below) will be the speed for max range.
To visualise the effect of wind, move the starting point of this line along the x-axis from the origin. Move it to the right for a headwind and to the left for a tailwind, in each case by the number of knots of headwind or tailwind. This new starting point will then produce a line which makes a tangent to the drag curve at a different speed to that for still air. The tangent will occur at a faster speed for a headwind and at a lower speed for a tailwind.
Much easier to see graphically than trying to explain it!
For a piston powered aircraft, the same can be done on the 'power required v speed' graph.