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 1,400 feet ahead of the first train is traveling at a constant speed of 96 feet per second and can be modeled by the function y = 96t + 1400. Solve the system of equations. Which solution represents a viable time that the trains are side by side?

14 sec
15 sec
16 sec
17 sec

Answer 1

14 sec

Explanation:

I got it right on the test.

Answer 2

14 seconds.

Explanation:

y = 14t^2

y = 96t + 1400

As the left sides of the equations are the same:

14t^2 = 96t + 1400

14t^2 - 96t - 1400 = 0

7t^2 - 48t - 700 = 0

We need 2 numbers whose product is (7*-700) = -4900 and sum to -48.

They are -98 and 50 , so we write:

7t^2 - 98t + 50t - 700 = 0

7t(t - 14) + 50(t - 14) = 0

(7t + 50)(t - 14) = 0

t = -7.142, 14

we ignore the negative solution so:

t = 14.