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

Question

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) 24

generis · Accepted Answer

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.

Bunuel · Answer

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 .

Answer: D.

mbaiseasy · Answer

N=\frac{20*2*(1}{2)*5280/600+40^{2}} 
 N=\frac{20 * 5280}{2200}=\frac{528}{11}=48

Answer: 48

AlphaMan21 · Answer

How come you wouldn't adjust the speed to 1/2 of 40?

Bunuel · Answer

Why should we do that? The average speed of the cars is 40 miles per hour means that the speed is 40 miles per hour for any portion of the highway (1/2-mile, 1-mile, ...).

MulanQ · Answer

(20*(5280/2)*2)/(600+1600)

eliminate 2 = 20*5280/2200 
eliminate 2 zero = 2*528/22 = approximately 2*500/20 = 1000/20 = 50 ---> D is closet

luckyme17187 · Answer

its very simple & straight stuff but took lot for time for me to understand it. :cry:

(40*5280) / 2 (600+40^2) = 48

AnsQ · Answer

I just ballparked to save time= (20*2*2650)=(600+1600), so (20*2*2650)/(2200), just divided by roughly 2200 to leave something like 20*2 left (but a little more). The only answer option close to 40 is 48. So answer D

Atul11 · Answer

What I don't understand about this problem is the following

If speed is in miles/hour and distance is in feet . Then why can't we convert feet into miles or vice versa and then perform the calculation ?

ENGRTOMBA2018 · Answer

You need to be economical with your choices in terms of both effort and time spent. Ideally, your best bet is to find a way that gives you the best ROI with least amount of time or energy spent.

Try to change minimum number of variables that will give you the correct answer. There is no 1 way for this question. You can approach it from either direction.

I did it by converting distance from miles to feet (thats it!). It was simple to do this conversion as d was 0.5, much simpler than having a d of 0.23 or 0.37 etc.

glt13 · Answer

This is an easy one to miss if you don't keep your math straight and don't read the instructions correctly

Let's give it a go

N = (20Ld) / (600+s^2)

L = 2
d = .5(5280) = 2640
s = 40
Plug and Play

N =  20(2)(2640) 
....... 600+1600

N =  20(2)(2640) 
..........2200

N = 2(2)(264) / 22
N = 2(2)(12)
N = 48

ScottTargetTestPrep · Answer

Although this problem may seem wordy and confusing, it has much more bark than bite. In the given equation, we have variables L, d, and S, and the entire equation is set equal to N.

We also are told the following:

N = the number of cars in a certain instant in time

L = number of lanes in the same direction

d = length of the portion of the highway, in feet

s = average speed of the cars, in miles per hour

We are given the following values for the variables:

d = ½ mile

L = 2 lanes

s = 40 mph

Before plugging these values into the equation, we must convert ½ mile to feet. Since we know that (5,280 feet = 1 mile), we know that:

½ mile = ½ x 5,280 = 2,640 feet

So now we can plug all this info into the equation to determine the estimated number of cars N.

N = (20Ld)/(600 + s^2)

N = (20 x 2 x 2,640)/(600 + 40^2)

N = (40 x 2,640)/2,200

N = (4 x 264)/22

N = (2 x 264)/11

N = 528/11 = 48

Answer D.

Note: Notice that at the end we kept reducing our equation so that we did not have to work with numbers that were too large; keep things as simple as possible.

mcelroytutoring · Answer

Attached is a visual that should help.

v1801philip · Answer

What i do not understand is: on the highways, cars go in two different directions, that is a common knowledge, so having to estimate number of cars  on the highway , not on the part of the highway that goes only in one direction, implies that number of lanes has to be multiplied by 2.
I think this is a clear miss in the problem wording, there is no leap of additional knowledge required, it is pretty much as taking for granted that sun rises on the east, yet for some reason problem gives it that highway has only one direction, which completely inconsistent with reality.

mcelroytutoring · Answer

If you read carefully, it says in the question that L represents the number of lanes  going in the same direction . You don't need to multiply the answer by 2, because the formula is for the number of cars traveling on a portion of a certain highway, which is exactly what you are solving for and thus the formula provided should have already accounted for that fact.

If for some reason the formula provided by GMAC were flawed or open-ended, then you still wouldn't be responsible for realizing that fact, so I suggest that you just trust the formula as it is.

"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 (...) 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)"

anox · Answer

Since the values in answer choices are reasonably far apart, approximation can get you answer pretty quickly.

=>  \frac{20 * 2 * 0.5 * 5280}{600 + 40^2}  =>  \frac{20 * 5280}{2200}  (on simplification)

\approx{\frac{20 * 5}{2}}  =>  10 * 5 
  ( 5280/2200\approx{5000/2000})

\approx{50}

Closest answer choice  (D) 48

dave13 · Answer

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 ?

Bunuel · Answer

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

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

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

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

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