## Suburban Ride-Sharing Is Mathematically Impossible

#### Joyce Park stashed this in Modern problems

**Stashed in:** Awesome, Math!, economics, Uber, math, Economics, Transportation, Mathy, Lyft

To save this post, select a stash from drop-down menu or type in a new one:

Does ride-sharing work in the suburbs? Let's do the arithmetic!

The math looks sound. The number of suburban people who would ride share rounds to zero:

- You have
10,000 peopleworking in downtown Palo Alto.- A zipcode in nearby Redwood City with a population of 31,500 residents is home to the largest share of commuters who work in downtown Palo Alto:
500.- If 10 percent of these commuters were willing to carpool to work, as per national averages, then the demand for a ride-share service is at most
50 people a day. (And that’s a generous assumption, since the vast majority of carpoolers are family members or coworkers, as opposed to complete strangers.)- If all 50 of these workers keep normal hours with standard morning commutes—again, a generous assumption—then they would all head to the office in a two-hour window. But since not everyone leaves for work at the same time, that window should be broken up into segments. Raney uses
six 20-minute segmentsfor the two-hour peak commute period.- The six segments turn Redwood City’s 50 potential ride-share users into groups of about eight. In other words,
eight out of 31,500 peoplein Redwood City might be matched for a carpool into downtown Palo Alto on any given morning.- If there are even just two competing ride-share services, that number halves to
four out of 31,500.

4:56 PM Nov 13 2015