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 seconds to stop, during which time the average speed
24
of the car is 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) x2 + 48x - 3,960 = 0
B) x2 + 48x - 7,920 = 0
C) x2 + 72x - 3,960 = 0
D) x2 + 72x - 7,920 = 0

The correct option is;

D) x² + 72·x - 7920 = 0

Step-by-step explanation:

The time it takes the car to stop = x/24 seconds

the average speed during stopping = x/2 feet per second

Given that the car was initially travelling at x feet per second and it takes the car 165 feet to stop after the driver takes 1.5 seconds at the initial speed x before the break is applied, we have;

Total distance traveled = (x/24)×(x/2) + x×1.5 = 165

= x²/48 + 1.5·x = 165

Multiply through by 48, we have;

x² + 72·x = 7920

Which gives the equation as follows;

x² + 72·x - 7920 = 0.

=

x=0.8898305 is the answer to that equation