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What I've Learned
Let's say you live one mile from work and that the speed limit along that route is 45 miles per hour.
One day you oversleep and are in danger of being late to work. To get there on time, you drive 70 miles per hour. Before you arrive, however, you are pulled over by the police and given a hefty ticket. Also, as a result of being stopped, you are 20 minutes late for work.
In life, it's not possible to turn back the clock, but in this column, it is, so let's back up.
One day you oversleep and are in danger of being late for work, but you stick to the 45 mph speed limit and arrive with a scant 60 seconds to spare. It was close, but you made it.
My question is: If you drove 70 instead of 45 – and managed not to get pulled over – how much earlier would you arrive? Seven minutes? Five minutes? Three minutes?
Not even one minute. The difference between driving one mile at 45 miles per hour and at 70 miles per hour is only 29 seconds. Hardly worth risking life or limb and a speeding ticket over.
I'm no longer the math wiz I once was. When it comes to stuff like this, my mental gears are a bit rusty and often need a sample problem to help figure out a forgotten formula.
Driving 60 miles at 60 miles per hour would take how long? Without lifting a pencil, I can say the answer. One hour. So what's the formula for figuring out time in such a problem?
I need to do something to 60 and 60 that will give an answer of one. If the two numbers are multiplied, it comes to 3,600 hours. That's not right. Try dividing. Ah. The answer is one. Very good. But do I divide distance (60 miles) by rate (60 miles per hour) or the other way around?
Doing another easy problem will tell. Driving 120 miles at 60 miles an hour takes how long? Again, without lifting a pencil, I can say the answer. It's two hours. And thus we see that dividing distance (120 miles) by rate (60 miles per hour) gives me time (two hours).
So, dividing one mile by 45 miles per hour gives a time of .022 of an hour. To convert this decimal into minutes, multiply by 60, which gives 1.33. The one is one minute. The .33, however, is .33 of a minute. To change this to seconds, again multiply by 60, which gives 19.8 seconds. Round up and we have a minute and 20 seconds.
Now let's do the same for 70 miles per hour. Divide one mile by 70 miles per hour and we get .01428 of an hour. Change this decimal into minutes by multiplying by 60. The answer is .857 of a minute. Again multiply by 60 to turn this into seconds. The answer is 51 seconds.
Subtracting 51 seconds from a minute and 20 seconds gives 29 seconds, the difference between driving one mile at 70 and driving it at 45.
Two things you can learn from this. To remember a forgotten math formula, create an easy problem that you know the answer to, then figure out what steps you'd take to get that answer. And driving at a faster rate over a short distance doesn't save much time.
My wife and I recently drove to Kentucky and back. Neither of us tend to speed and often use cruise control to help keep us honest. Long stretches of the route had a speed limit of 70 mph. On a trip, say of 1,000 miles, what's the time difference between driving the whole way at 55 and driving it at 70?
I won't drag you through the math, but will just give the answer. Driving 1,000 miles at 55 mph takes a little over 18 hours. Driving it at 70 takes about 14 hours and 20 minutes, a difference of three hours and 40 minutes.
Needless to say, we were thankful for those 70 mph stretches, which cut a chunk off our time behind the wheel.