Solution
Given the parametric equation for Andy and Donald path below
For Andy; Where t in on the interval (0, 50)
[tex]x(t)=24+\frac{2}{3}t,y(t)=8+\frac{1}{6}t[/tex]
For Donald; Where t in on the interval (0, 50)
[tex]x(t)=12+t,y(t)=5+\frac{1}{4}t[/tex]
To find out if they collide, we equate either x(t) or y(t) of Andy and Donald as shown below
Equating x(t) of Andy and Donald gives
[tex]24+\frac{2}{3}t=12+t[/tex]
Solve for t
[tex]\begin{gathered} 24+\frac{2}{3}t=12+t \\ 24-12=t-\frac{2}{3}t \\ 12=\frac{1}{3}t \\ 12=\frac{t}{3} \\ Crossmultiply \\ t=12\times3=36\text{ seconds} \\ t=36\text{ seconds} \\ Since\text{ t is in tenth of seconds} \\ t=36\times0.1=3.6\text{seconds} \\ t=3.6\text{ seconds} \end{gathered}[/tex]
Hence, Andy and Donald will collide at 3.6 seconds
