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# At a certain instant in time, the number of cars, N

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VP
Joined: 22 May 2016
Posts: 1136

Kudos [?]: 407 [2], given: 647

At a certain instant in time, the number of cars, N [#permalink]

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28 Oct 2017, 06:56
2
KUDOS
At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula

$$N=\frac{20Ld}{600+s^2}$$

where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a 1/2-mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile)

(A) 155
(B) 96
(C) 80
(D) 48
(E) 2

tusumathur1995 wrote:
shouldn't the speed=40 miles per hr, be converted into feet?

tusumathur1995 , I can see why you might think so, but no. If you remain unconvinced after this post, run the numbers the way you suggest. No answer choice is even close.

Take the formula exactly as it is given, even if seems odd.

The task here is much like strange symbol problems: given a rule and some numbers, can you plug the numbers in while following the rule and get the right answer? That's it.

The formula defines speed, $$s$$, without reference to feet: "$$s$$ is the average speed of the cars, in miles per hour"

Only $$d$$ mentions feet: "$$d$$ is the length of the portion of the highway, in feet"

In this formula, $$d$$'s units and $$s$$'s units have nothing to do with one another. It might seem as if they should.

Again, take the formula exactly as it is written.

See mcelroytutoring, above - you are not responsible to discern the logic of a given formula.

So if given a formula written by the test writers, with clearly defined variables, (that is not a conversion question, e.g., 50 ft/sec = how many mi/hr?), take the formula and its variables at face value.

If the test makers define a variable a certain way, we must do the same.

Hope that helps.

Kudos [?]: 407 [2], given: 647

Intern
Joined: 09 Mar 2016
Posts: 49

Kudos [?]: 5 [0], given: 50

Re: At a certain instant in time, the number of cars, N [#permalink]

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11 Nov 2017, 08:25
Bunuel wrote:
At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula

$$N=\frac{20Ld}{600+s^2}$$

where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a 1/2-mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile)

(A) 155
(B) 96
(C) 80
(D) 48
(E) 2

Given:
L = 2 lanes;
d = 1/2*5,280 feet;
s = 40 miles per hour.

Thus, $$N=\frac{20*2*\frac{1}{2}*5,280}{600+40^2}=48$$.

Bunuel hello, one question; Why did you write so d = 1/2*5,280 feet; D is distance of highway right and 5280 is one mile in feet...I dont understand why are you combining these two things?

I understand this word problem like this:
L = 2 lanes;
d = 1/2x
s = 40 miles per hour.
no ?

Kudos [?]: 5 [0], given: 50

Math Expert
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135874 [0], given: 12715

Re: At a certain instant in time, the number of cars, N [#permalink]

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11 Nov 2017, 08:29
dave13 wrote:
Bunuel wrote:
At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula

$$N=\frac{20Ld}{600+s^2}$$

where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a 1/2-mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour? (5,280 feet = 1 mile)

(A) 155
(B) 96
(C) 80
(D) 48
(E) 2

Given:
L = 2 lanes;
d = 1/2*5,280 feet;
s = 40 miles per hour.

Thus, $$N=\frac{20*2*\frac{1}{2}*5,280}{600+40^2}=48$$.

Bunuel hello, one question; Why did you write so d = 1/2*5,280 feet; D is distance of highway right and 5280 is one mile in feet...I dont understand why are you combining these two things?

I understand this word problem like this:
L = 2 lanes;
d = 1/2x
s = 40 miles per hour.
no ?

d is the length of the portion of the highway, in feet.

1/2-mile = 1/2*5,280 feet.
_________________

Kudos [?]: 135874 [0], given: 12715

Re: At a certain instant in time, the number of cars, N   [#permalink] 11 Nov 2017, 08:29

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