At a certain instant in time, the number of cars, N, traveling on a portion...

AAPL wrote: ↑

Mon Feb 03, 2020 3:25 am

GMAT Paper Tests

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

OA D

Given:

• L = 2 lanes;
• d = 1/2*5,280 feet = 2640 feet;
• s = 40 miles per hour

Thus,

$$N=\dfrac{20Ld}{600+s^2}=\dfrac{20*2*2640}{600+40^2}=48$$

The correct answer: D

Hope this helps!

-Jay
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AAPL wrote: ↑

Mon Feb 03, 2020 3:25 am

GMAT Paper Tests

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

OA D

We are given the following:

N = the number of cars on the highway portion at 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 information into the equation to determine N, the estimated number of cars.

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 2,64)/22

N = (2 x 264)/11

N = 528/11 = 48

Answer: D