Asad wrote:
BrainLab wrote:
A certain truck uses \(\frac{1}{12}+ kv^2\) gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses \(\frac{5}{12}\) gallon of fuel per mile?
(1) The value of k is \(\frac{1}{10800}\).
(2) When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.
Hello experts,
EMPOWERgmatRichC,
VeritasKarishma,
IanStewart,
Bunuel,
chetan2u,
ArvindCrackVerbal,
GMATGuruNY,
GMATinsightWhat if the
highlighted part is removed from the question prompt or it says 'k' is not 'constant'? Should the correct choice be A?
Also, if the highlighted part is not removed from the question prompt, can we say the rephrased version is something like ''what is k''? If yes, can you explain 'how'?
Thanks__
Hello Asad,
I understand your effort to experiment by trying to look at a problem from different angles by trying cases similar, albeit with minor changes, to the ones defined in the problem. This is a great way of learning a lot from a given problem. However, there’s always a thin line between doing something and overdoing it. As such, you need to be extremely aware of this line. Otherwise, you will end up overthinking about the question, which is not a good thing to do.
In this case, making k as a variable will just invalidate the question.
Fuel consumption = ½ + k\(v^2\) for a certain truck. Apart from the velocity v, let’s assume that the variable ‘k’ accounts for all other influencers like load carried, number of people, tyre pressure, road conditions etc., If we kept ‘k’ as a variable, then it would be humanely impossible to answer this question knowing that there may be hundreds of variables that influence the fuel consumption.
That’s probably why the equation defines the fuel consumption as a function of velocity and nothing else. Higher the velocity, greater the consumption and vice versa.
Also, the question is not about finding ‘k’. It’s about finding ‘v’ at which the consumption is 5/12 gallons per mile.
Hope that helps!