Midlife dilemma of the day: how long are you morally obliged to stay on a trip to the park?

When you first take your first child to a park, there is indeed a certain magic in it: seeing their little face light up as they clamber up the steps of the slide, then elbow another toddler off the top... But by the time that child is eleven, the novelty of taking subsequent siblings has worn off and you realise that parks, at least the ones with playgrounds rather than ornamental gardens or contemporary sculpture, are just really dull.
So how long should you be expected to sit there, staring at the sky, hoping it will rain and give you a legitimate get-out? 15 minutes? 20 minutes? A whole hour? Is there some sort of equation whereby time spent in this grassy purgatory must be directly proportional to the sum of the activities on offer and distance from your house, multiplied by the square root of the ambient temperature and number of snacks you remembered to take? And does it make you a bad parent if you refuse to go in goal, or tell them they are old enough to push themselves on the roundabout?