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

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02 Dec 2012, 08:02

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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)

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

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02 Dec 2012, 08:02

Expert's post

Walkabout 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.

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

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25 Jun 2013, 02:41

Expert's post

AlphaMan21 wrote:

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

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, ...). _________________

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

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12 Oct 2013, 09:42

Bunuel wrote:

Walkabout 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.

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

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11 Sep 2014, 03:12

Walkabout 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

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

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

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24 Nov 2014, 11:19

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

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

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

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01 Aug 2015, 13:50

Expert's post

Atul11 wrote:

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 ?

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. _________________

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

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03 May 2016, 05:31

1

This post received KUDOS

Walkabout 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

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. _________________

Jeffrey Miller Scott Woodbury-Stewart Founder and CEO

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