The one time I went to the West Ranga, some 12 years ago, there were four of us sharing two rods as two pairs. As each beat on the river fishes two rods, we had a beat to ourselves. And as has been suggested by others, we changed over every half hour or after every fish, whichever came first (I think 15 minute spells would definitely have been too short). It worked well, but we were four friends who had fished together a number of times, and I wouldn't consider any of us greedy or competitive fishers, so the likelihood of friction was never going to be great. Sometimes one's slot might only last a couple of casts; you might find that frustrating, but bear in mind that if the fish are 'on' the chances are that you'll be back in soon enough. And at worst you're only going to be sitting on the bank for half an hour, which allows time for a cup of coffee or a drink. In an ideal world one would want to have fishers of roughly equal ability sharing, but if it's a blind date that cannot be guaranteed.
As a general point, be aware that there is always the potential for friction, and do your best to avoid it. In fishing (as indeed in any other area of life), you should always try to be considerate to others. Don't be greedy or selfish! In particular, bear in mind that not only will you be sharing your rod, but you'll also be sharing the beat with another rod (or even another two sharers), and you must always give a thought them. A couple of sharp-elbowed rod sharers could easily set out to get more than 50% of the fishing on a two rod beat, inevitably be to the detriment of the other rod. You may feel you want to get your money's worth from the expensive fishing, but they, too, are entitled to their money's worth so you should always make sure they get an equal share of the fishing.
One specific about rod sharing is that, in my book, if a rod is to be shared it should be fished as closely as possible to how a single rod would fish it. That means that two sharers can't be positioned away from one another, communicating only by phone, and it certainly doesn't mean that one rod can fish down the best bit of the beat while his partner stands at the top of the same bit waiting to start, effectively blocking out the second rod or pair of rods! So when you change over, the second rod should start where the other rod has finished (or slightly further downstream). If the other rod(s) happen to be following you down, going in upstream of where your partner has stopped is a definite no-no. And when one rod lands a fish, the other one shouldn't be waiting like a sprinter in the blocks to start in as soon as the fish hits the net. A solo rod would naturally take a moment to look at the fish and exchange a word with the guide before restarting, and two rods sharing should try to observe a similar rhythm.