How much time does speeding save?

Bob has a simple commute: he drives 60 miles, traffic-free, on a highway.

Normally Bob drives with the flow of traffic at 70 miles per hour.

One day he is anxious and instead speeds at 80 mph. How much time does he save?

How much time would he save at 90 mph?

The formula to use

This problem can be easily solved using grade school math.

The formula to remember is:

Distance = Speed * Time

But we have to make a couple adjustments for our purposes. First, we have to rearrange the equation and solve for time.

Then we want to have the answer in minutes. Since speed is expressed in miles per hour, we will divide speed by 60 to get “miles per minute.”

The formula we will use is:

Time(minutes) = Distance / (Speed in mph/60)

How much time does Bob save?

We can substitute the numbers to find out the time saved. Here is a table of the results.

SPEED VS TIME TAKEN FOR 60 MILES
Speed (mph) Time (minutes)
70 51.4
80 45
90 40

As you can see, Bob only saves at most a tad over 10 minutes by driving at an excessively fast pace of 90 mph. Speeding is just not a big time saver.

The extra risk from speeding

Even though speeders save little no time for themselves, their decision does have a larger effect of putting everyone else at risk.

According to the Department of Transportation publication here, speeding related accidents costs us over $40 billion per year.

Speeding is one of the most prevalent factors contributing to traffic crashes. The economic cost to society of speeding-related crashes is estimated by NHTSA to be $40.4 billion per year. In 2009, speeding was a contributing factor in 31 percent of all fatal crashes, and 10,591 lives were lost in speeding-related crashes

Additionally, a fast car is more dangerous to pedestrians and others around. As the Australian Academy of Science cautions against speeding here:

Once a pedestrian has been hit by a car, the probability of serious injury or death depends strongly on the impact speed. Reducing the impact speed from 60 to 50 kilometres/hour almost halves the likelihood of death, but has relatively little influence on the likelihood of injury, which remains close to 100 per cent. Reducing the speed to 40 kilometres/hour, as in school zones, reduces the likelihood of death by a factor of 4 compared with 60 kilometres/hour, and of course the likelihood of an impact is also dramatically reduced

Hard to argue with that.

A selection bias

One of my greatest worries is a selection bias that happens with this type of argument.

Anyone that’s smart enough to understand the math I just presented is likely already smart enough to know it’s a bad idea to speed.

And conversely, lecturing someone that speeds with equations is unlikely to produce results.

The worst part is that if enough people speed, it actually becomes dangerous to drive the actual speed limit. You are essentially forced to go a little bit faster to avoid getting hit by faster drivers.

Unless we have a concerted effort to get everyone to drive slowly, fast drivers force us to join them and be unsafe. Alas, it’s just another one of the ways that stupid people can make fools of us all.



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  • Michael

    I’m not sure what you mean when you say “he drives 60 miles, traffic-free, on a highway,” because then you turn around and say “Normally Bob drives with the flow of traffic”. What traffic? You said the highway is traffic free. :-)

    In any case, this reminds me of a fun little puzzle I heard a long time ago:
    Bob drives 30 miles an hour for 1 minute, at which point he suddenly decides to turn around and race back his starting point fast enough to average 60mph (speed, not velocity) for his round trip. Assuming he turns around and instantly accelerates to this new speed, how fast does he have to average on the way back to meet his goal?

  • Peter P

    I don’t disagree about the maths behind speeding, and certainly slower speeds equals less risk of injury once hit. However, the argument that driving fast = unsafe I think warrants deeper thinking.

    To take the oft quoted ‘rule’ that slow speed = less injury death to it’s logical conclusion: Make all cars travel at zero speed and you will have a perfect safety!

    The real issue that no-one focusses on is not how to prevent injury once you have an accident – it’s how you should prevent an accident in the first place. I work in IT and once of the tasks that are drilled into us any time we have a problem is to identify the ‘root cause’ – and to fix that, not the symptoms.

    Reducing speed to reduce injuries once an accident has occurred is treating the symptoms – not the root cause.

    Germany has their autobahns where there are no speed limits and their accident rate is quite low. Roads are properly designed, drivers are attentive (cos of the speed), pedestrians are kept separated.

    I despair when I see the lazy arguments put forth that if you go over the speed limit you are a dangerous driver. It’s such a superficial argument that we’ll never actually meaningfully reduce accident rates (and hence injuries) if people just gloss over the complexities of how we will actually make long term improvements (without going back to the buggy and cart).

    I’ll leave you with one final point. Who is the safer driver? The driver doing 70kmph in a 60kmph zone driving on a clear day … or the driver doing 60 kmph in a 60kmph zone whilst it’s thunderstorms and torrential rain?

  • Eyal

    The reason that speeding is so popular despite the very bad outcomes is because the probability of a very bad outcome is so low. We have a hard time judging the expected value of events that are so infrequent.

  • tgt

    Like Peter P, I have to attack the laziness of this argument.

    For starters, anytime there is accident with one car speeding, speeding is listed as a cause of that accident… even if they’re T-Boned by someone running a red light or a truck falls on them from an overpass. The statistics related to speeding are bunk. It’s a circular argument.

    Second, the mixed units is just flat out deceiving. You go from MPH to KPH. Statistics about the death rate going from 37MPH to 31MPH have no bearing on the difference between 70MPH and 90 MPH. Did you mean for this post to be a bunch of non sequitors?

    Third, the selection bias section exists, but doesn’t talk about the actual selection bias in the previously quoted statistics.

    This is like the anti-speeding side in a middle school debate… if the debaters were idiots.

  • Alan

    But speeders spend less time on the road and therefore have a somewhat mitigating reduction in exposure to accidents, right?

  • http://www.quantitativepeace.com M. Allen

    You should also add in the cost. Typically, with higher speeds, your MPG is going to be altered as well. I am sure we can factor in the difference in fuel consumption, the distance, and the direct cost (assuming a price per gallon). Then we can translate that cost into “time to work off the extra gas”. It may be marginal, but it should factor into that decision calculus.

  • Ben Sauer

    Well, you’ve already been pilloried a fair amount, so let me just pile on lightly while we await your backing off.

    If Bob saves 6.4 minutes per direction per day over 200 days, then he’ll save about 2600 minutes. Which is roughly 44 hours. Assuming he’s up about 15 hours a day, we’re talking about 3 full days saved by driving what quite possibly is a more natural speed for the road.

    Consider that many speed limits are set not for safety reasons but for political or revenue purposes. This is why the same road in the same quality switches from 70 to 65 as one crosses the Columbia River into Oregon. And the same road switches from 65 to 75 as one crosses the Snake into Idaho.

    It’s about 842 miles from Seattle to Salt Lake. 240 in Washington most if at 70 (20 miles are at 60 in King County and about 5 more are 60 near Yakima). 208 miles are in Oregon mostly at 65 though some sections slow to 55. 277 in Idaho at 75 (very brief slowdown through Boise). 70ish in Utah at 75 and 50 ish at 65. Working those numbers through it should take 12 and a quarter hours to drive. Assuming a couple of stops for gas of 20 minutes each. A couple of bathroom breaks of 15 minutes each. Two meals of 30 minutes each. And we’re at a trip of 14 and 1/2 hours.

    If one drives it more aggressively, and shaves 90 minutes off the drive, it’s only a 13 hour trip. Can you calculate the increased safety from only travelling 13 hours versus 14.5 and compare it to the minimal risk incurred by traveling faster? Given that the danger curve for driving has to go up the more tired someone is, that last 90 minutes has to be particularly useful time to save.

  • Christopher Chow

    http://www.internationaltransportforum.org/irtad/pdf/risk.pdf

    This is data that backs up Peter’s post regarding the autobahn in Germany. What’s nice about this data is they actually tell you the fatality rate weighted by miles driven and also by person– so you know that you are comparing apples to apples.

    I think it will be very difficult to use speed reduction as an accident reduction public health initiative. At least, it would be difficult to make the case regarding actual impact of reducing speed to reduce fatalities. Why?

    The key is the frequency of fatal accidents themselves.
    We all understand that IF we are in an accident, lower speed would generally lead to better survivability. But the actual frequency of accidents is low enough that when most of us decide whether to speed or not, it doesn’t weigh heavily.

    A better spin (to accomplish the same goal –> get people to not speed) is to do what M Allen suggested above: target the wallet. Indeed there is a local maximum for fuel economy at highway speeds — any higher and you trade off MPGs for your MPH. What that exact maximum is, i suspect actually may depend on your car — although there are random data out there attempting to illustrate the trends in MPG vs MPH.

    And as a side note –I still occasionally speed during wintertime. But I hedge and have snow tires on my car. Germany actually requires this on their highways and apparently if you are in an accident and don’t have them on during winter, it affects your criminal charges and also your insurance.

    Root cause analysis is interesting — I’m not sure how easily the techniques can be applied to car accidents. Typicaly, they are employed by organizations (particularly health care and business) to figure out how some snafu happened. its a lot of man hours spent deconstructing the incident. Think of it like NHTSA descending on train accidents with accident deconstructionists, investigators, etc. Just impractical to do this for every accident.





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