Why Speeding Doesn’t Help: Math for Everyday Use

Some like to claim that math isn’t useful in everyday life. I offer up a little math for a practical situation: Does speeding really get you there faster?

By the way, I’m showing rounded results below, but I calculated the results before rounding.

Case #1: Local Road

A local road I often travel has a 45 mph speed limit and plenty of traffic lights. On a recent drive, I gathered some numbers. I drove 7.7 miles on this road, passing through 17 traffic lights. Other cars were on the road too, but traffic wasn’t heavy. The weather was fine for driving. My only delays were the traffic lights. I went 45-50 mph when I was rolling.

It took me just over 15 minutes to cover 7.7 miles. My average speed was only 30 mph (average speed = miles traveled / hours traveled), because when I’m stopped at a light, I’m going 0 mph. If I could have gone 45 the whole time, I’d have covered 7.7 miles in just over 10 minutes. In other words, those 17 traffic lights made my travel take 50% longer (15 minutes instead of 10 minutes).

What if I wanted to get my travel time down to 10 minutes instead of 15? How fast would I have to go?

Speeding in the car doesn’t make the traffic lights cycle any faster, so let’s guess for the moment that I’d still have 5 minutes of delay due to traffic lights, no matter how fast I went. That means I’d have to cover 7.7 miles in 5 minutes. Miles / hours = mph. 5 minutes = 5/60 hours = 0.083 hours. That leads to: 7.7 miles / 0.083 hours = 92.4 mph. I’d have to sustain a speed of 92.4 mph, more than double the speed limit! That’s impossible on that road, and it would be insane to try.

What if I could sustain 55 mph? That would have been hard on this trip, because of other cars. I’d have had to weave aggressively to get through, and I still probably would have spent some time behind cars going under 55. But if I could have done it, it would have taken 8.4 minutes to drive 7.7 miles. Add in the 5 minutes of delay for traffic lights, and I’ve gotten my 15-minute drive down to 13.4 minutes. In other words, aggressive driving would have saved me only a little time.

In fact, the delays due to traffic lights might have gone up if I went 55 mph. Those 17 lights weren’t all for major intersections. Many of them were for little side streets; most of those lights were green when I got to them. If they’re sequenced for 45 mph traffic, speeding just means I rush to the next red light, which won’t turn green until the 45 mph traffic catches up. Aggressive driving might not save me any time at all, if every red light means the slower drivers catch up with me again.

Case #2: Beltway

To get to one brother’s house, I use the Capital Beltway. According to mapping sites, the drive should take 29 minutes to travel 17.3 miles. That’s realistic. Average mph = miles / hours, and 29 minutes is 0.483 hours, so 17.3 / 0.483 = 35.8 mph. That’s slower than one might expect, considering that over half of the distance is on a 55 mph highway, but it’s correct.

Let’s say, though, that this time I’m leaving the house 5 minutes later than I intended. I want to make up for it by speeding on the Beltway. The mapping site says I’d have 9.5 miles on the Beltway. At 55 mph, I’d take 10.4 minutes to cover the distance. How fast would I need to go get that down to 5.4 minutes? 5.4 minutes = 0.09 hours. Mph = miles / hours, so 9.5 miles / 0.09 hours = 105.6 mph. I’d have to average over 100 mph on the Beltway, just to get to my brother’s house a few minutes earlier. If you’ve ever driven on the Beltway, you’d know it’s insane or impossible to go that fast. And that’s just to get there at 2:00 instead of 2:05. Not worth it.

Case #3: Interstates

Now I want to drive to Williamsburg, Virginia, so my wife and I can have a nice weekend getaway. We’ve picked out a hotel. The mapping sites tell me it’s 171 miles of driving, and it should take 2 hours and 49 minutes. Most of the driving will be on interstates, where the speed limit will be 55 mph and up.

Let’s take a closer look at the directions and see how much time and distance will be on the interstates. I’d travel 3.9 miles (10 minutes) before I get to a highway. At the other end of the trip, I’d spend 2.8 miles (7 minutes) off the interstates. Everything in between is on interstates. That leaves 171 miles – 3.9 miles – 2.8 miles = 164.3 miles on the interstates, and 2 hours 49 minutes – 10 minutes – 7 minutes = 2 hours 32 minutes of traveling on the interstates. Traveling 164.3 miles in 2 hours and 32 minutes gives an average speed of 64.9 mph on the highways.

How much time can we gain by speeding on the interstates?

If we travel 10% faster, the 64.9 mph would become 71.3 mph. Could we average that much speed on over 150 miles of highway? I’m not so sure, but if we could, the 2 hours and 32 minutes would drop to 2 hours and 18 minutes. By averaging more than 70 mph over a long distance, we could save a mere 14 minutes. Would an extra 14 minutes open up new opportunities for enjoying Williamsburg? Nope.

Besides, what are the chances of averaging that much speed? Pretty low. If you’ve ever driven on I-95 between DC and Richmond, or I-295 around Richmond, or I-64 between Richmond and Williamsburg, you know that traffic jams are a very real possibility. We’d have to average more than 70 mph. In other words, if we’re stuck at slower speeds for some of the time, we’d have to go way faster than 70 mph to make up for it. Occasionally hitting 70 wouldn’t be enough. And this is all to save a measly 14 minutes. It doesn’t seem worth it.

Do the Math: Speeding Doesn’t Help

There you have it. Three different situations, and speeding makes no significant difference in any of them. Speeding might feel like you’re making better progress, but when you factor in traffic lights, traffic volume, and the fact that speeding is really only a few percentage points above the speed limit anyway, the math shows that speeding doesn’t make a big difference in travel time. Thank you, math.

Jim

 

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