Question

I need help with this practice problem solving The subject for this practice today is “parametric equations” Grade level is 11th

Answer 1

Given the parametric equation for Andy and Donald path below

For Andy; Where t in on the interval (0, 50)

`x(t)=24+(2)/(3)t,y(t)=8+(1)/(6)t`

For Donald; Where t in on the interval (0, 50)

`x(t)=12+t,y(t)=5+(1)/(4)t`

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

`24+(2)/(3)t=12+t`

Solve for t

`\begin{gathered} 24+(2)/(3)t=12+t \\ 24-12=t-(2)/(3)t \\ 12=(1)/(3)t \\ 12=(t)/(3) \\ Crossmultiply \\ t=12*3=36\text{ seconds} \\ t=36\text{ seconds} \\ Since\text{ t is in tenth of seconds} \\ t=36*0.1=3.6\text{seconds} \\ t=3.6\text{ seconds} \end{gathered}`

Hence, Andy and Donald will collide at 3.6 seconds