Which comes full circle back to your belief that the cart travels the same distance through the air as it does over the ground.
For those that don't get it ... and I didn't understand it at first.
By definition, the cart is travelling in the same direction as the wind, but a little faster.
It makes it a little easier to follow, however, if you use the cart as your frame of reference instead of the ground.
If the cart is facing left, the ground will be moving under the cart at some speed from the left to the right. Let's call that speed x.
Since the cart was moving a little faster than the wind speed, from the perspective of the cart, the air will be moving from the left to the right also. But, the speed of the wind passing the cart will be less than the speed of the ground.
Speed is distance divided by time. From start to finish, the time for all three things, cart, wind, and ground are the same. Since the speeds of the ground and wind are different, the distance the ground and wind travel must be different. Therefore, the cart travels a different distance through the wind than it does on the ground.
Another way to understand this is to think of the cart going the same speed and direction as the wind. In relation to the wind, the cart is not moving. And, in relation to the cart, the wind is not moving. But, the ground is moving. Therefore, the cart must be travelling a different speed and distance through the air than along the ground.
If it makes it easier to understand ... replace the cart with an airplane. As the pilot of the plane, how would you determine how fast you're going if you couldn't see out of the cockpit (using your eyes, gps, radar, etc.) and couldn't ask someone outside the plane? You could open a window and see how fast the wind blows in. But, what would that tell you? It would tell you how fast you are moving through the air, but, because the air itself is moving, it won't tell you how fast you are moving in relation to the ground. In any kind of wind, the ground speed and air speed of the plane are different. The same thing is true of the cart.
-- Roger