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# A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee

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A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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Updated on: 03 Feb 2016, 22:01
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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.

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Originally posted by BrainLab on 19 Sep 2015, 14:26.
Last edited by Bunuel on 03 Feb 2016, 22:01, edited 2 times in total.
Renamed the topic and edited the question.
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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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11 Oct 2015, 12:24
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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 gallon of fuel per mile.

The question is (1/12)+k(v^2)=5/12 (1). V-?
From st.1 we know k hence we can find v. Sufficient
From st.2 v=30 and (1/12)+k(30^2)=1 Hence we can find k and solve equation (1). Sufficient
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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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16 Jan 2017, 16:07
2
You can solve this problem without doing any math.

Understand you're given 1 equation w/ 2 variables (k & v). To rephrase the Q, you need to find one variable to get the answer here.

(I) Gives you 1 variable (K). With this, you can find V. sufficient.
- Elim BCE

(II) Gives you equation: (1/6) = 1/12 + (30)^2(k). 30=V, so since they (indirectly) gave you (V), you can find (K). sufficient.
- Elim A

Ans: D
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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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07 Feb 2016, 14:35
1
Consumption of fuel= 1/12+ kv^2

1. It gives you the actual value for the constant k, therefore you are able to find v from the original question. SUFFICIENT
2. It gives you: 1/6 = 1/12+ k30^2 , therefore you could find k and the use this to find v. SUFFICIENT

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.

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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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20 Dec 2017, 07:26
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1
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.

We need to determine v when:

5/12 = 1/12 + kv^2

4/12 = kv^2

1/3 = kv^2

Statement One Alone:

The value of k is 1/10,800.

Thus, we have:

1/3 = (1/10,800)v^2

3600 = v^2

60 = v

Statement one alone is sufficient to answer the question.

Statement Two Alone:

When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.

Thus:

1/6 = 1/12 + k(30)^2

1/12 = 900k

1/10,800 = k

Since we have determined the value of k (the very same value of k in statement one), we can determine v. Statement two alone is sufficient to answer the question.

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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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17 Dec 2015, 11:59
Each of statement give us components to complete the equation and find the asked. This is sufficient to conclude that Each Statement is sufficient instead of finding the real values.

IMO D
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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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22 Jan 2016, 01:53
Does statement (2) basically state that when driving at 30 mph, the truck uses ONE gallon per mile? Think the language set me off here
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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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07 Feb 2016, 14:35
Consumption of fuel= 1/12+ kv^2

1. It gives you the actual value for the constant k, therefore you are able to find v from the original question. SUFFICIENT
2. It gives you: 1/6 = 1/12+ k30^2 , therefore you could find k and the use this to find v. SUFFICIENT

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.

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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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18 Jan 2017, 22:02
In fact, doing the actual calculation here will be very time consuming and un-necessary.
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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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01 Mar 2017, 22:34
you have two unknowns in one equation - v and k.

a. gives you the value of one unknown - k - so you can calculate v - sufficient
b. gives you the value of v (can be computed with information given) - so you can derive the value of k - sufficient.
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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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25 Sep 2017, 17:36
Statement 1 asks us to solve an equation with a squared variable, so why are there not two solutions? I thought equations to the second power always had two solutions. I answered B for this one.
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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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25 Sep 2017, 21:15
ThisandThat wrote:
Statement 1 asks us to solve an equation with a squared variable, so why are there not two solutions? I thought equations to the second power always had two solutions. I answered B for this one.

v is the speed of the truck. Can it be negative?
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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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14 Dec 2017, 16:29
Hi All,

We're told that a truck uses 1/12 + (K)(V^2) gallons of fuel per mile when its speed is V miles per hour and that K is a constant.
We're asked for the speed at which the truck travels so that it uses 5/12 gallon of fuel per mile.

To start, we can input the specific 'fuel usage' that the question asks us to deal with into the given equation:

5/12 = 1/12 + (K)(V^2)

Thus, to figure out the speed (V), we need to know the constant (K).

1) The value of K is 1/10,800

Fact 1 gives us the constant, we can figure out the value of V (and since we can't have a "negative speed", there's only one value for V^2 - the positive one).
Fact 1 is SUFFICIENT

2) When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.

We can plug this information into the equation, which gives us...

1/6 = 1/2 + (K)(30^2)

With this equation, we can then solve for K (which we could then plug back into the original question and solve for V).
Fact 2 is SUFFICIENT

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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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27 Jul 2018, 01:44
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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.

We have to work for:
(1/12) + kv^2 = 5/12

Option (1) K is given so we have to work for only v. Sufficient.
(2) we will get k from : (1/12) + k(30)^2 = 1/6, putting k in the original equation ((1/12) + kv^2 = 5/12) we will get v. sufficient

Ans. D.
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Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee  [#permalink]

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16 Nov 2019, 15:15
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.

1/12 + kv^2 gallons/mile -----> v miles/hour
5/12 gallons/mile -----> ?

(1) 1/12 + kv^2 = 5/12, if we know k, we know v... SUFFICIENT
(2) 1/6 gallons/mile -----> 30 miles/hour
1/12 + k.30^2 = 1/6, solve for k. put value of k in the equation to solve for v.... SUFFICIENT

Ans: D
Re: A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee   [#permalink] 16 Nov 2019, 15:15
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