## Friday, September 10, 2010

### Distances, Part IV

It's Friday so let's finish off the week AND our review of measuring distances. Sometimes, instead of measuring reality, we are asked to estimate total distance formerly traveled, or forecast total distance to be traveled in the future. For example, each year I get a letter from my insurance company asking,

Q1. How far do you drive your cars? We want to calculate the (higher) premium for next year.

Of course I don't want to over-pay them, so I don't want to over-estimate my travel.

A1a. Given the distance to work which I measured yesterday, we could simply calculate like this:

For my Honda commuting car, I estimate:

52 weeks x 5 days a week x 50 miles per day = 13000 + 2,000 extra = Approximately 15,000 miles

To confirm this, I re-calculate in a different way. I've owned the car for 3 years 4 months (40 months). It has 55,000 miles now and already showed 8,000 when I bought it. Now for the math:

55,000 - 8,000 = 47,000 ÷ 40 = 1175 per month x 12 = 14,100 miles per year. So 15,000 is reasonable.

Here's another  question:

Q2. How many miles do I drive the Honda each day, on average?

A2. I can also calculate this using several methods:

A handy website tells me that it's been 1308 days since I bought my car, so 47,000 ÷ 1308 = 36 miles. Another way to check is to use my insurance forecast of 14,100 ÷ 365 = 38.6 miles/day. Close enough.

A1b.  For our Volvo, I calculate from actual experience.

The Volvo hit 60,000 miles this week. I bought it new in May 2002. That's roughly 8 years and 4 months, or 100 months. Simple division shows I've driven it 600 miles per month on average. That's 7,200 miles per year.

Notice that these distances were not measured directly using any measuring tool; we derived the distances using the odometer, the calendar, an internet calculator, and our elementary school arithmetic!

Q3. Most Excel Math deliveries to schools go in two white trucks. What is the average mileage traveled PER delivery?

A3. We have no idea. We keep track of the cost per box, not the number of delivery trips OR the miles to each school. We can't measure distances if we don't have the data.