Speeding on the Road Does Not Save that Much Time: A Mathematical Analysis
How many times while driving on the highway do other drivers fly pass you and you are going at or at least 10 mph over the posted speed limit? To me it happens very often that in a span of about five miles I believe about 25 or more cars would have passed me like I am hardly moving. When I see this I often murmured to myself “Why are these people driving so fast when I know it will not make that much difference time wise”.
At that moment I am thinking mathematically and doing some quick mental calculations in my head. We know we have laws in place in the United States that prohibit texting while driving but there is no law that say no calculating while driving. Well, anyway I will prove in this article my point on driving faster does not save that much time unless you are driving extremely fast which will probably make matters worse for the guy since he is putting himself at a higher chance of getting into accident or even not making it to his destination alive.
Proving My Point with Simple Math
Before we can begin the calculations let me put out one very important assumption in place. All calculations are based on constant speed going from point A to point B. Of course in the real world no one drives at constant speed but it is much easier to calculate speed and other attributes of a moving object. Doing the calculations in the real world would require monitoring all the variables involved when we are traveling from point A to point B such as traffic movement, acceleration and deceleration rate intervals, rest stop breaks, etc. But I do not think any of this really matters because all the drivers on any given highway are generally affected for miles by the same variables more or less. So the time saved with respect to other drivers on the same highway probably is insignificant as my calculations will show in the two scenarios presented below.
Scenario 1: Driving For 100 Miles
Let us begin with the first scenario. Suppose Driver A and Driver B are driving to the same destination 100 miles away from their starting point. Driver A is driving at a constant speed of 65 mph and Driver B is driving at a constant speed of 75 mph to get there. How much time does Driver B save with respect to Driver A?
Some of us know the following simple physics equation to calculate constant speed, “Speed = Distance / Time” or as words “speed = distance divided by time” but we need to calculate “time” in this case. We already know the speed and distant, therefore, we must rearrange the equation to calculate the “time” required to transverse the 100 mile distant. The new equation is:
“Time= Distant / Speed” or as words “Time = distance divided by speed”
Driver A: Time = 100 miles / 65 mph = 1.54 hours so 1.54 hours = 92 minutes
Driver B: Time = 100 miles / 75 mph = 1.33 hours so 1.33 hours = 80 minutes
now subtract the two times to get the difference in the arrival time between the two drivers.
92 minutes - 80 minutes = 12 minutes
Results: Driver B would only beat Driver A by a measly 12 minutes after driving 100 miles.
The another way of looking at this, if Driver A drives for 1 hour at a constant speed of 65 mph he would have driven 65 miles while Driver B at the speed of 75 mph would have driven 75 miles. The two drivers would be 10 miles apart in one hour. In terms of distance that is a lot but in terms of time they are less than 10 minutes apart. That is not much time difference when Driver A finally reach the 75 mile mark. It would be less than 10 minutes later for him.
Looking back at the first scenario, if you wish to determine how far apart the drivers are when Driver B reach the 100 mile mark here are the calculations.
We already know Driver B would have driven 100 miles at a constant speed of 75 mph in 80 minutes. Also we know 80 minutes equal 1.33 hours. All we need to do is determine how far Driver A would have driven in the same time at 65 mph from the same starting point.
First we have to rearrange the constant speed equation to calculate distant this time.
Speed = Distance / Time
Rearrange the equation to calculate distant. Therefore Distance = Speed X Time.
Results: Distance = 65 mph X 1.33 hours = 86 miles
Therefore, Driver A is 14 miles behind when Driver B reaches his destination at the 100 mile mark, but in terms of time he is only 12 minutes away and Driver B was doing all that speeding for 80 minutes and consuming more gas in the process just to save 12 minutes.
Now I can apply these calculations to a must longer distant like 1000 miles by simply multiplying all our results from Scenario 1 by 10 using the same speed as before for Driver A and Driver B.
Scenario 2: Driving 1000 miles
This time Driver A and Driver B are driving to the same destination 1000 miles away from their starting point. Driver A is driving at a constant speed of 65 mph and Driver B is driving at a constant speed of 75 mph to get there. How much time does Driver B save with respect to Driver A?
Driver A would reached his destination 1000 miles away in 15.4 hours or in 920 minutes while Drive B would reached the same destination in 13.3 hours or in 800 minutes. As you can see after driving 1000 miles at a constant speed of 75 mph Driver B would reach his destination 120 minutes or 2 hours earlier than Driver A who was driving at 65 mph. The time saved is a little better than the previous scenario with the shorter distant but Driver B had to drive 1000 miles in 13.3 hours to save 2 hours over the slower driver.
As you can see there is not much time saved in driving faster to get from point A to point B. In order to see a significant savings in time when it come to traveling by car from point A to point B on a typical highway, Driver B must almost literally drive two times faster than Driver A to see a significant saving in time. In other words, Driver B must drive at a constant speed of 130 mph to cut the time in half to 7 hours 42 minutes assuming Driver A is still driving at a comfortable, safe constant speed of 65 mph to reach his destination 1000 miles away. In reality it take about 18 hours to travel 1000 miles in the United States despite the fact you drive at speeds up to 75 mph but not for the entire trip. Furthermore, the time saved between the two drivers get closer to zero as the distances between point A and point B get shorter no matter what speeds they are going even if the speed is not constant for the entire distant.
© 2012 Melvin Porter