## Friday, October 9, 2009

### Driving is math-ing me crazy

So there we were on vacation in England, and it seemed like the gas (they call it Petrol) cost about ten bucks a gallon, but we must have gotten 50 miles per gallon!

It cost a fortune to fill up but it still seemed cheaper to drive. Why don't we get those cars over here?

Thus began a conversation with a friend of mine. He was looking for information and didn't know how to go about doing the conversions.

Let's look at the math.

Depending on how he kept records and how the car was set up, we probably need to convert liters (litres) to gallons, pounds sterling to dollars, and potentially kilometers to miles and UK gallons to US gallons.

THE FACTS OF THE CASE
His receipt said he purchased 49.56 litres at 102.9 per/litre = £51.00.

A discount coupon saved £2.45 for a net price of £48.55. Of that, £6.33 was VAT tax; £42.22 fuel.

The distance traveled was 603 miles (not kilometers, although the car could display either).

The country was England.

The date was July 11, 2009.

The dollar/pound exchange rate that day was £1.00 = \$1.62560

THE CALCULATIONS
Money
Let's do the money first. He paid with a US credit card that charges a 3% fee for international purchases.

The cost in dollars is calculated like this £48.55 x 1.62560 = 78.92 + 2.37 (3%) = \$81.29

Fuel
We'll do the fuel quantity next. He bought diesel, NOT petrol.

The quantity is 49.56 x 0.2641 (to get US gallons) = 13.1 US gallons

(To get UK gallons, it's 49.56 x 0.22 = 10.9 UK gallons)

Cost per gallon
The cost per gallon was \$81.29 / 13.1 = \$ 6.21

Miles per gallon
603 miles / 13.1 US gallons = 46.03 miles per US gallon
603 miles / 10.9 UK gallons = 55.32 miles per UK gallon

Cost per mile
The cost per mile is 81.29 / 603 = \$ .13

THE COMPARISON
The comparison is with his vehicle here in the United States.
The latest fill-up cost \$66.00 at \$3.039 per gallon, for 21.72 gallons.
The car traveled 467 miles on that tank.

Miles per gallon
467 / 21.72 gallons = 21.5 miles per US gallon

Cost per mile
The cost per mile is 66.00 / 467 = \$ .14

THE VERDICT

It was cheaper to drive in the UK, because of the much greater fuel economy of the 2010 VW Golf tdi and his discount coupon. Without the coupon saving £2.45, the cost per mile would have been equal.

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