Question

The position of a passenger train that is traveling at an initial speed of 14 feet per second and continues to accelerate can be modeled by the function y = 14t2. A second train that is 1,200 feet ahead of the first train is traveling at a constant speed of 130 feet per second and can be modeled by the function y = 130t + 1200. Solve the system of equations. Which solution represents a viable time that the trains are side by side?

A. 14 sec
B. 15 sec
C. 16 sec
D. 17 sec

Answer 1

Solving the system of equations, it is found that a viable time that the trains are side by side is given by:

B. 15 sec

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

$y = 14t^2$

$y = 130t + 1200$

They will be side by side when:

$14t^2 = 130t + 1200$

$14t^2 - 130t - 1200 = 0$

It's solution is a quadratic function with coefficients a = 14, b = -130, c = -1200, hence:

$\Delta = (-130)^2 - 4(14)(-1200) = 84100$

$x_1 = \frac{130 + \sqrt{84100}}{28} = 15$

$x_2 = \frac{130 - \sqrt{84100}}{28} = -5.71$

Time is a non-negative measure, hence option B is correct.

More can be learned about a system of equations at https://brainly.com/question/24342899