Writing Equations

Link of the Day

New things can be exciting, but also scary.  Several years ago, Y2K (the year 2000) frightened many people.  Now people are worried about the end of the Mayan calendar on Dec 21, 2012.  Take a look at this article to see how people are reacting to rumors about the end of the world.  How could you use this current event on an SAT essay?  It would easily relate to questions about whether the world is getting better, how people understand themselves and those in authority, feelings and rationality, and many other topics.  Make sure to pick out specific details to mention in your essay if you choose this as one of your current event examples!

Algebra: Writing Equations

Read the following SAT test question and then select the correct answer. 

Always read math problems carefully so that you don’t miss an important piece of information.  Identify the bottom line, and assess your options for reaching it.  Choose the most efficient method to attack the problem.  Many problems have multiple steps, so be sure to loop back and make sure that you solved for the bottom line.

The stopping distance of a car is the number of feet that the car travels after the driver starts applying the brakes. The stopping distance of a certain car is directly proportional to the square of the speed of the car, in miles per hour, at the time the brakes are first applied. If the car’s stopping distance for an initial speed of 20 miles per hour is 17 feet, what is its stopping distance for an initial speed of 40 miles per hour?

Bottom Line: d (distance) = ?

Assess your Options:  You have to decide how to use the information in this problem; in other words, you need to write an equation.  Plugging in the answer choices will take a lot of guess work.  Instead, carefully work through each piece of information that you are given.

Attack the Problem:  You have probably worked with distance, rate, and time before.  One formula that is often used in Knowsys classes is distance = rate × time.  This problem is asking you to write a similar equation.  The problem says: “The stopping distance of a certain car is directly proportional to the square of the speed of the car, in miles per hour, at the time the brakes are first applied.”  In other words, you know that distance is (is means equals in math) directly proportional to something.  Now pay particular attention to the part that says “directly proportional.  This phrase just means that when the distance gets bigger, so does the other side of your equation.  For that to happen, you need another constant number on the other side of the equation.  Your distance is equal to some constant number times speed squared.  Your formula should look like this:

distance = constant number × speed²

Now that you have written an equation to show what is happening in this problem, you are ready to look at the next piece of information.  Plug in the first situation in which an initial speed of 20 miles per hour results in a distance of 17 feet.

d = c × s²
17 = c × 20²

Now you can solve for c by isolating the variable.  Use your calculator when it will be faster than mental math.

17 = c × 400  (divide each side by 400)
.0425 = c

Now you have enough information to find your bottom line. Plug in the second situation in which the car is going 40 miles per hour and solve for the distance.

d = c × s²
d = .0425 × 40²
d = .0425 × 1600
d = 68

Loop Back:  You solved for the stopping distance of a car traveling 40 mph, just as the question asked.  You are ready to look at your answer choices.

(A)  34 feet
(B)  51 feet
(C)  60 feet
(D)  68 feet
(E)  85 feet

The correct answer is (D).
On, 39% of the responses were correct.

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