A certain car averages 25 miles per gallon

[leonitrof]

In most countries of the world, the fuel consumption is expressed in Liters required to drive 100 kms, or L/100 kms.

Many on-line converters are available on the web to convert one consumption rate into the other, but no easy method, that could be used by a simple 4-basic-function pocket calculator.

Here it is :

Just remember the "magic" number 235.

This is a one-step method that works both ways :

235 / mi./gal. = L/100kms

and as well :

235 / L/100 kms = mi./gal.

This is due to the fact that any numbers of mi./gal. and corresponding L/100 kms, when multiplied one by the other, give a constant product :

235.2141128......

Using 235 gives a result accurate to 3 decimals (actually between 1 and 2 thousanths). Enough by far for any day-to-day use.

The "magic" number is obtained by multiplying the number of liters in a gallon and the number of miles in 100 kilometers. Doing the math will show you how the result is actually the constant product revealed here.

[RPurewal]

leonitrof, that's a neat little shortcut should one ever encounter a need to perform such a conversion in the course of daily life -- but what does it have to do with the problem in this thread?

[JohnHarris]

I know this is an old problem but it does come up again and again and it was the subject of the recent edition of gmatters. So I though I would comment. First the magic number 235. That because, if you transform the measurements into km and L/km, you can do the weighted average. However, a previous post and the following (which is basically a repeat) gives another way to do 'the same thing' with no conversion necessary.

A 'trick' to use on these kind of problems is to first look at the units of the problem. You are given a number of miles and a number of miles per gallon. You should recognize almost immediately that multiplying the numbers won't work because you are going to get a weird unit like miles^2/gallons. What happens though if you invert one set of the givens, i.e. make the givens miles and gallons per mile.

We then have
A certain car averages 1/25 gallons per mile when driving in the city and 1/40 gallons per mile when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and 50 miles on the highway? The weighted average to get the number of gallons used is
10 miles * 1/25 gallons/miles + 50 miles * 1/40 gallons/miles
= (10/25 + 50/40) gallons = 1.65 gallons
Divide by the miles driven and we get
1.65/60 gallons/mile or 60/1.65 mpg
If you can remember 1.6 (or 1.62 or 1.645 or ...) is about 1/6 of 10 = .6, then 60/1.65 is about .6 * 60 / 10 or about 36.

Note: This is really just dividing miles by miles per gallon so nothing new has been added. However, looking at the units of the problem and thinking about your answer for a couple of seconds can (help) keep you from making misteakes.

[RPurewal]

You are given a number of miles and a number of miles per gallon. You should recognize almost immediately that multiplying the numbers won't work because you are going to get a weird unit like miles^2/gallons.

this is a good observation -- if you are stuck on a word problem, then a quick analysis of the units in which the quantities are expressed may yield the key to a correct procedure.