what does it mean when you see a math question that asks you the shortest possible distance? it's confusing.

Question

i have this easy math problem, but the question is tricky for me. i always get this kind of question in my physics class too.

Hershey's car gets 24 miles per gallon of gasoline and Wynmark's truck gets 18 miles per gallon. When travelling from berlington to white river they both use a whole number of gallons of gasoline. What is the shortest distance possible between burlington and white river?

hope u cud help me with this. thanks!! =) hahahaha by the way.. this is my brother's problem, not mine. and i feel so ashamed. hahaha =)

Answer 1

You want
24m = 18n

You factor
24 = 2^3(3
18 = 3^2(2)

The LCM of 24 and 18 is 3^2(2^3) = 72

Therefore, the shortest distance is 72 miles.

Answer 2

Distance is length. Travelling a certain length will consume fuel. The engine itself has a certain rate of fuel consumption. If you adjust the fuel consumption rate of the engines to equal* 0 or 1 in the problem, the car that then uses the least gas will have travelled the shortest route.

The question itself appears to be phrased incorrectly because the shortest possible route has nothing to do with the facts in the case, and needs to be analyzed from mapping. See Mapquest or Yahoo maps.

Well, now that I looked at the other answers, I can see that there is a least "possible" distance equation. But it's not a real number. Reality is quite different from a calculation and if a driver were to use this as an average, it would fail to be useful in business or in practical life situations.

This question is theoretical and it should say not least possible distance but the theoretical least distance. In terms of probability, using actual data, the result may show to have a very low probability and approx. an impossible result.
Therefore the term "possible" is questionable.
I take exception to the accuracy of this math book in its teaching terms.

I don't think you need to be ashamed of misunderstanding these terms, because I believe that the texts that are in use are very poor quality at this time. For now on tests all you can do is
use the expressions that they expect.

*0 or 1 is used depending on the equation

Answer 3

What's Up Shiela?
If there is no map involved the first part of the problem must be an attempt to obfuscate the reader.You know how you and your brother always answer C on your tests?From now on when you see "the shortest distance" think straight line.

Answer 4

The shortest distance between two points is always a straight line. The other information in this word problem is insignificant to the question.

Answer 5

i'm not going to flame you, Karen. i will purely say that your naivete and gullibility in believing that somebody is dropping time with vast, acceptable-flying crop dusters spreading some unknown chemical into our environment stands out in finished array mutually as you publish this nonsense to a public talk board like YA. there is not any astounding international conspiracy to spray crap into the air. and easily thinking the undeniable fact that there are planes flying at greater altitudes than your KLM flight does not miraculously turn them suited right into a sinister plot. recover from your self. fairly makes me marvel purely what that is which you're arising on that farm . . .

Answer 6

using an integer # of gallons, the car can go
24, 48, 72... miles
the truck can go
18, 36, 54, 72... miles.
The answer is 72 miles.

Answer 7

find out what the LCM (lowest common multiplier) between the mpg of the two cars is; so basically the LCM of 18 and 24. this will find your answer for you.

hope this helps!