A car is traveling at x feet per second. The driver sees a red light ahead, and after 1.5 seconds reaction time, the driver applies the brake. After the brake is applied, the car takes x/24 seconds to stop, during which time the average speed of the car is x/2 feet per second. If the car travels 165 feet from the time the driver saw the red light to the time it comes to a complete stop, which of the following equations can be used to find the value of x?
A) x^2 + 48x − 3,960
B) x^2 + 48x − 7,920
C) x^2 + 72x − 3,960
D) x^2 + 72x − 7,920
During the 1.5-second reaction time, the car is still traveling at x feet per second, so it travels a total of 1.5x feet. The average speed of the car during the x/24 second braking interval is x/2 feet per second, so over this interval, the car travels (x/2)( x/24)= x^2/48 feet. Since the total distance the car travels from the time the driver saw the red light to the time it comes to a complete stop is 165 feet, you have the equation
x^2/48 + 1.5x = 165.
This quadratic equation can 48 be rewritten in standard form by subtracting 165 from each side and then multiplying each side by 48, giving x^2 + 72x − 7,920, which is choice D.
Some questions on the SAT Math Test will ask you to solve a quadratic equation. You must determine the appropriate procedure: factoring, completing the square, the quadratic formula, use of a calculator (if permitted), or use of structure.
You should also know the following facts in addition to the formulas in the directions:
1. The sum of the solutions of x^2 +bx+c=0 is −b.
2. The product of the solutions of x^2 +bx+c=0 is c.
Each of the facts can be seen from the factored form of a quadratic. If r and s are the solutions of x^2 +bx+c=0, then x^2 +bx+c=(x−r)(x−s). Thus, b = −(r + s) and c = (−r)(−s).
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