[0] https://pupster.files.wordpress.com/2008/01/dog-translator.j...
To be precise: not all communication is language, language involves grammar, which hasn't (yet) been conclusively demonstrated in any other species.
Source: was a neuroscientist who TAed for a guy who tried to teach a chimp language in the 70's.
They can also transmit cooperation information non-verbally, by posture for example, so your experiment testing for speed would test two things, possibly cancelling each other. It's possible that the verbal communication exists but lowers the efficiency of the cooperation (maybe one of them is yelling at the other how stupid he is and that they should use his superior technique).
> During the trials when one dolphin opened the canister unaided, one or more of the other dolphins was present nearby, watching the task. On these occasions, there was no increase in chatter.
[0] http://www.sheldrake.org/about-rupert-sheldrake/blog/rat-lea...
The obvious experiment here is to have two groups of dolphins positioned so that they can hear each other but not see each other; give one the puzzle, and then, later, give the other the same puzzle. If the second group solves it consistently faster than the first one then probably information is being transferred. (Although it could just be that the second group is more motivated after hearing the first group get excited about something.)
Actually arranging an ethical but meaningful experiment with bottlenose dolphins, which are quite big and are highly opinionated, is left as an exercise for the reader...