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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 [#permalink] New post 02 Dec 2012, 07:02
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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)

(A) 155
(B) 96
(C) 80
(D) 48
(E) 2
[Reveal] Spoiler: OA
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Re: At a certain instant in time, the number of cars, N [#permalink] New post 02 Dec 2012, 07:02
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.

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

Answer: D.
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Re: At a certain instant in time, the number of cars, N [#permalink] New post 19 Dec 2012, 05:29
N=\frac{20*2*(1}{2)*5280/600+40^{2}}
N=\frac{20 * 5280}{2200}=\frac{528}{11}=48

Answer: 48
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Re: At a certain instant in time, the number of cars, N [#permalink] New post 24 Jun 2013, 18:25
How come you wouldn't adjust the speed to 1/2 of 40?
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Re: At a certain instant in time, the number of cars, N [#permalink] New post 25 Jun 2013, 01:41
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, ...).
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Re: At a certain instant in time, the number of cars, N [#permalink] New post 12 Oct 2013, 08:42
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.

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

Answer: D.



Hi

Is there any shortcut to the calculation?
It took me about 40 seconds to calculate and that's precious time wasted....
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At a certain instant in time, the number of cars, N [#permalink] New post 28 Aug 2014, 15:19
ronr34 wrote:

Hi

Is there any shortcut to the calculation?
It took me about 40 seconds to calculate and that's precious time wasted....


(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

Last edited by MulanQ on 12 Sep 2014, 12:51, edited 1 time in total.
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Re: At a certain instant in time, the number of cars, N [#permalink] New post 11 Sep 2014, 02:12
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. :cry:

(40*5280) / 2 (600+40^2) = 48
Re: At a certain instant in time, the number of cars, N   [#permalink] 11 Sep 2014, 02:12
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