Context
-------

A warlock in the game that I run suffers from two levels of [exhaustion](https://www.dndbeyond.com/sources/basic-rules/appendix-a-conditions#Exhaustion):

> 
> Level 1: Disadvantage on ability checks
> 
> 
> Level 2: Speed halved
> 
> 
> 

This warlock knows the spell *[levitate](https://www.dndbeyond.com/spells/levitate)*. He is *so* tired—it's a [hangover from a very potent homebrew drug, named Flashberries](https://rpg.stackexchange.com/q/144746/42805)—that he levitates himself slightly to alleviate his body by hovering instead of walking. Yesterday, instead of walking/floating around by himself, he held onto the shoulders of his ranger ally and let the ranger "pull" him forward (as the ranger walked at normal speed).

Ruling
------

When the players came up with this idea, I ruled that this method of movement is possible. Because the warlock is afloat, the spell doesn't burden the ranger with extra carrying capacity while the warlock is not using his *own* movement, so both the ranger and warlock could now move at normal speed. The ranger effectively pulls forward a seemingly weightless person.

I thought it was quite the clever plan to avoid this part of his exhaustion, and I didn't want to slow down gameplay by looking up the rules, so I ruled in favor of the party.

Research & Question
-------------------

Now that I'm reading up on both the spell description and [What form of movement is granted by Levitate cast on yourself?](https://rpg.stackexchange.com/q/140472/42805), I realize we might've misunderstood how *levitate* works. Zooming in on the relevant parts (emphasis mine):

> 
> The target can move only by pushing or pulling against a **fixed object or surface** within reach (such as a wall or a ceiling), which allows it to move as if it were climbing.
> 
> 
> 

and

> 
> If you are the target, **you can move up or down** as part of your move. 
> 
> 
> 

So this makes me think that the answer to my question would be **No, because the ranger is not a fixed object or surface.** And since spells only do what they say they do, I'm more inclined to think that, by RAW, the ranger is unable to move the warlock *at all*. It also looks like the warlock is also not able to actually hover horizontally by using this spell (oops).

Could anyone give a clear yes or no to my question, by RAW? And if either of my interpretations are incorrect, please explain why that is.