Conversely, service time is often quite predictable. A network router can ship a data packet in a fixed period; a cashier needs only so much time to ring you up; or in an example salient to the issue at hand, most mammals bigger than rats need roughly 21 seconds to clear their bladders. Humanity’s penchant for clothing and privacy has added time to its whiz clock, and led to a significant disparity in service times for males and females going number one. Rogiest has actually done the math: On average, men take one minute to pee. Women take about a minute and a half. As you might have guessed, men’s ability to remain standing and mostly dressed while urinating explains some of the difference. But women don’t just have to undo more clothing and more complicated clothing—ever try to bundle a romper?—they also have to open and close doors, as well as wipe the seatie, sweetie.

However, the biggest reason women waste more of their lives queuing for the bathroom is that the world has a surfeit of facilities that serve men. Urinals take up much less space than individual stalls. Diving into the literature on bathroom design, Rogiest and a colleague found that the average men’s room has 20 to 30 percent more toilets than the average women’s room. So, those long lines at the women’s room aren’t just from clothing logistics and extra cleanliness. Women just have fewer places to pee.

The Golden Ratio

Rogiest actually tested how this disparity in bathroom service times and available toilets cost women more time. To set a baseline, he and his co-author Kurt Van Hautegem created a model where men and women had the same number of toilets and arrived in line at 10-second intervals. The only variable changed between the two sexes was in service times. With a 60-second service time, they found that men waited an average of just 1.52 seconds. Women, with a minute and a half service time, waited about a minute.

Then they started playing with bathroom layouts: changing the ratio of urinals to squatters, giving women more toilets than men, and toggling whether the bathrooms were segregated or not. They also upped the intensity of the arrival times to mimic a concert or movie letting out. Their ideal outcome would be short, and mostly equal wait times for both sexes. They found a pretty steady pattern: “It basically comes down to there is a bottleneck whenever you separate the sexes,” he says. When the bathrooms had no fixed gender, however, the sex-specific bottleneck disappeared, and everyone spent about 2 minutes, 10 seconds in line.

But they actually got their best results when they offered that fast lane for stand-up pee-ple. Let’s see if you can figure out the ideal ratio, in the context of an airplane-based word problem: You have 300 people on a five-hour flight. Everyone will need to pee twice, half of them taking 60 seconds, half taking 90 seconds. One-third will have to poop once, which (let’s be optimistic) takes five minutes. If this plane comes standard with six single-occupant sit-downers, how many would you replace with Durinals to reach the optimum pee times for everyone?

Savvy readers might have figured out a shortcut to all of this: Call Zodiac Aerospace and ask them. Too bad 1) this is cheating, and 2) Zodiac did not respond to my emails. To calculate an exact answer, you’d probably need sophisticated software using Markov randomization sequences to simulate how quickly people line up and then clear out from each “operation.”

Luckily we have common sense and a scientist here to help. First, common sense. If you replace half of the commodes with urinals at a two-for-one discount, you’re going to wind up with mostly empty urinals and three very overburdened commodes. That’s unfair to half the plane’s passengers, with added discomfort for men who must advertise when they’re going to be sitting a spell.