In this why are we not converting speed to feet?

[email protected] wrote:plug these values into the formula and solve.

Rich

In this question I am confused that why are we not converting speed to feet(its in mile only)?

[email protected] wrote:70. 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,
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 aA-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 = 1mile)

This is a question from OG12 and is pretty straightforward. You have not copied it correctly.

The correct question states "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=(20*L*d)/(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)"

Solution:
N=(20*L*d)/(600+s^2)
L = 2
d = 1/2 miles = 1/2 * 5280 feet
s = 40 miles/hour

N = 20*2*1/2*5280/(600 + 40^2)
= 20*2*1/2*5280/(600 + 1600)
= 20*5280/2200
= 5280/110
= 528/11
[spoiler]= 48[/spoiler]

The question explicitly says that d is in feet and s is in miles per hour.

Cheers

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 + 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

We are given 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 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 264)/22

N = (2 x 264)/11

N = 528/11 = 48

Answer D