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Should I Stay, Should I Go?

Should I Stay, Should I Go?

That age-old question of whether it’s best to wait for the bus or start walking has finally been answered with science – the answer? Stay put! Dave Hall investigates.

It’s one of life’s big dilemmas – if you just miss the bus, do you wait for another one to come along? Or make a start and walk? Wait for what may seem like an eternity? Or turn and walk only to be overtaken by the bus after a couple of minutes?

Well, lucky for us, some American researchers have done some sums to help us make the right choice. And it’s good news for the lazy amongst us.

The mathematicians who carried out the study, Scott Kominers of Harvard University, and Justin Chen from the California Institute of Technology, concluded that only if no bus was due for an hour or more and your destination was less than a kilometre away was it worth walking. In all other cases, stay by the bus stop and wait patiently.

The problem reared its head while Chen was travelling to Kominers’ house to discuss some maths problems (as you do). The bus route covered the journey and Chen preferred taking the bus when possible, but was also conscious of being late should the bus not arrive on time.

After much discussion, the resulting paper, called “Walk Versus Wait: The Lazy Mathematician Wins”, contains the formula for the journey, which takes into account several factors including:

d - the distance in miles you have to go.
vw - walking speed.
vb - the bus’s speed.
tb – the time the bus arrives.

With two bus stops, the decision is easy; you should only walk if d/vw < tb + d/vb. For those who are less adept at maths and formulas, that means being lazy and waiting for the bus almost always makes sense. Using some altogether trickier maths, the plucky number-smiths showed that, even if you start making the bus routes more complicated and adding more and more bus stops, the conclusions stay the same.

Whether this theory works in London, where bendy buses are frequently held up by long traffic queues and even longer road works, is another matter. However, if you do decide to walk, do so immediately and briskly and don’t look back!

If you're interested, you can see the research paper here. However, it might be safer to stick to more from the Null:

- Useless - A knotty problem is unraveled
- Frightening - Mathelete's super brain
- Brilliant - Science solves tiddlywinks
- Please me - Procrastination is just some maths away
Image: Nick Cowie

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11 Jun 2011
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