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 = (20Ld)/(600+ s²)
where:
L is the number of lanes in the same direction,
d is the length of the portion of the highway, in FEET
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
The prompt instructs us to estimate the value of n BASED ON THE FORMULA.
In the formula:
d is in terms of FEET.
s in in terms of MILES per hour.
Thus, we must plug the following values into the formula:
L=2. (Since there are 2 lanes.)
d=2640 (Since 1/2 mile = 2640 feet.)
s=40. (Since the average speed is 40 miles per hour.)
Result:
N =
= (20*2*2640)/(600 + 40²)
= (20*2*2640)/(600 + 1600)
= (2*2*264)/(6+16)
= (2*2*264)/22
= (2*2*12)
= 48.
The correct answer is
D.
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