For a couple years I had a 45-minute commute, mostly by freeway, and it made me wonder how much time I could I save by speeding. Typically I stay pretty close to the speed limit since I've never found it that difficult either to leave early enough or to accept being late, and I derive a lot of mental ease from not being in a hurry and not having to worry about getting caught speeding. But I tend to do a lot of mental math on solitary, low-stress drives, and how much time I could save by speeding was some of it.

Rate times time equals distance, so given two speeds and the same distance, we have two different times:

To find the time saved by driving faster, solve for *t _{2}*:

Most of the southern part of Michigan's lower peninsula has speed limits of 70 miles per hour. On a 45-minute commute at 70 mph, driving 75 mph instead would give me a commute of

To me, 75 mph feels a lot faster than 70 mph, so I was surprised to realize that over 45 minutes it would only save me three minutes of travel time.

Of course, on a longer trip those small amounts of time add up. I've driven Canada's 401 to New England several times, and the speed limit is 100 kilometers per hour, though almost everyone seems to drive 120 kph. On a 14-hour drive,

On a 14-hour drive, a tired driver may be more dangerous than a slightly faster driver, so saving two hours by speeding could be the safer option on long drives, but good luck explaining your way out of a ticket with that reasoning.

These days I more commonly drive about 40 minutes on mostly 55-mph country roads. Occasionally someone will pass me going 60 or 65. Given the length of my drive (and probably theirs), speeding just doesn't seem worth it. Here's a chart of the time speeding saves on different length drives:

Speed (mph) | 10 min | 15 min | 20 min | 25 min | 30 min | 35 min | 40 min | 45 min | 50 min | 55 min | 60 min |
---|---|---|---|---|---|---|---|---|---|---|---|

56 | 10s | 16s | 21s | 26s | 32s | 37s | 42s | 48s | 53s | 58s | 1m |

57 | 21s | 31s | 42s | 52s | 1m | 1m | 1m | 1m | 1m | 1m | 2m |

58 | 31s | 46s | 1m | 1m | 1m | 1m | 2m | 2m | 2m | 2m | 3m |

59 | 40s | 1m | 1m | 1m | 2m | 2m | 2m | 3m | 3m | 3m | 4m |

60 | 49s | 1m | 1m | 2m | 2m | 2m | 3m | 3m | 4m | 4m | 5m |

61 | 59s | 1m | 1m | 2m | 2m | 3m | 3m | 4m | 4m | 5m | 5m |

62 | 1m | 1m | 2m | 2m | 3m | 3m | 4m | 5m | 5m | 6m | 6m |

63 | 1m | 1m | 2m | 3m | 3m | 4m | 5m | 5m | 6m | 6m | 7m |

64 | 1m | 2m | 2m | 3m | 4m | 4m | 5m | 6m | 7m | 7m | 8m |

65 | 1m | 2m | 3m | 3m | 4m | 5m | 6m | 6m | 7m | 8m | 9m |

The same math applies if you're headed to an appointment and realize with, say, 10 minutes to go that you're going to be a couple minutes late. Driving 10 mph faster at that point is only going to get you there one minute earlier.

We'll complicate this simplistic model in the next post.