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## Are we there yet?

Ever been driving and wonder how much longer you will be on the road? Or how much sooner you’ll get there if you speed up? If so, keep reading. Some simple math can help you figure it out while driving – and it can help pass the time since the inputs to the equation change every second you move down the road.

The first piece of data you need is the distance left to travel. This could be the miles to the next town or rest stop, or the final destination, or a random distance – like, say, 100 miles.

Next, choose the speed you are driving. An average speed will be fine, since we all know it is hard to stay at a constant speed for long.

The basic formula is (distance remaining) / speed = time remaining.

Here is an example to get the time remaining to travel 100 miles at 65 mph (note that the ‘miles’ cancel out to leave the units in ‘hours’):

$100\text{ miles / 65}\text{ mph} = 1.33 \text{ hours or about 1 hour and 32 minutes}$

If this was your current remaining time at 65 mph, how would it change if traffic clears up and you can average 5 mph faster? Here is how to compute the difference:

$100\text{ miles / 70}\text{ mph} = 1.43 \text{ hours or about 1 hour and 26 minutes}$

So the difference is 92 minutes at 65 mph, or 86 minutes at 70 mph

$92 \text{ minutes} - 86\text{ minutes} = 6 \text{ minutes (roughly)}$

Although this is a basic example and shows the process, it has some division that is hard to do in your head while driving. While driving, do some basic rounding and estimation to get easier numbers to work with (or yell out the numbers to the teenager in the car texting away on their cell phone…). One way to do this is to try using numbers for your speed that divide easily into the distance. For example, if you had 240 miles to go, try using 80 mph and 60 mph to get and idea of the time remaining at those two speed and estimate your time based on this reference difference.

Or, try getting an idea of how much time it takes to travel an easy reference distance (using the equation above, for every 100 miles at 75 mph it takes 80 minutes, and for every 100 miles at 80 mph it takes 75 minutes) then divide your remaining distance by 100, and use this answer to multiply by the corresponding minute value (400 miles left to drive, divided by 100 = 4. At 75 mph, that would be 4 x 80 minutes = 320 minutes, or 5 hours and 20 minutes. That is 5 hours and 20 minutes of driving, don’t forget to add time for potty breaks and food and fuel stops!

Always drive safely! Now that you have a method for looking at the time saved by speeding up, you can now decide if the extra time is worth the risk of going 5 mph faster and possibly getting a speeding ticket or worse, having an accident.