Question

Andy and Donald are both running toward the soccer ball during a game.

Andy's path is represented by the parametric equations x(t)=24+23t,y(t)=8+16t, where t is on the interval [0,50] and t is measured in tenths of seconds.

Donald's path is represented by the parametric equations x(t)=12+t,y(t)=5+14t, where t is on the interval [0,50] and t is measured in tenths of seconds.

Do the boys collide? If so, when do they collide?

Andy and Donald collide at 2.4 seconds.
Andy and Donald do not collide.
Andy and Donald collide at 3.6 seconds.
Andy and Donald collide at 4.8 seconds.

Answer 1

The answer is C. Andy and Donald collide at 3.6 seconds.

Answer 2

Correct option: second one -> Andy and Donald do not collide.

Explanation:

To find if the boys collide, we need to find if there is a common value of t where the their x position are equal and their y position are equal. To do this, we make x(t) of Andy equal to x(t) of Donald, , then if there is a value for t, we do the same for y(t) and check if the values of t are equal:

24 + 23t = 12 + t

22t = -12

t = -0.5455 seconds

As the time is negative, it will not occur, so the boys will never collide.

Correct option: second one