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

tusumathur1995 wrote:

shouldn't the speed=40 miles per hr, be converted into feet?

tusumathur1995 , I can see why you might think so, but no. If you remain unconvinced after this post, run the numbers the way you suggest. No answer choice is even close.

Take the formula exactly as it is given, even if seems odd.

The task here is much like strange symbol problems: given a rule and some numbers, can you plug the numbers in while following the rule and get the right answer? That's it.

The

formula defines speed, \(s\),

without reference to feet: "\(s\) is the average speed of the cars, in

miles per hour"

Only \(d\) mentions feet: "\(d\) is the length of the portion of the highway,

in feet"

In this formula, \(d\)'s units and \(s\)'s units have nothing to do with one another. It might seem as if they should.

Again, take the formula exactly as it is written.

See

mcelroytutoring,

above - you are not responsible to discern the logic of a given formula.

So if given a formula written by the test writers, with clearly defined variables, (that is not a conversion question, e.g., 50 ft/sec = how many mi/hr?), take the formula and its variables at face value.

If the test makers define a variable a certain way, we must do the same.

Hope that helps.