Hello, lilikoipssn!

Car A and Car B leave the origin at noon.

Car A travels north at 66 mph and car B travels east at 112 mph.

(a) How far apart are they after 1 hour?

(b) How far apart are they after $\displaystyle t$ hours?

(c) When are they 1300 miles apart? We can solve all the problems at once . . . Code:

P *
| *
| * d
66t | *
| *
| *
* - - - - - - - - *
O 112t

Car $\displaystyle A$ drives north at 66 mph.

. . In $\displaystyle t$ hours, it has gone $\displaystyle 66t$ miles to point $\displaystyle P$

Car $\displaystyle B$ drives east at 112 mph.

. . In $\displaystyle t$ hours, it has gone $\displaystyle 112t$ miles to point $\displaystyle Q.$

Their distance $\displaystyle d$ is the hypotenuse of right triangle $\displaystyle POQ.$

. . $\displaystyle d \;=\;\sqrt{(66t)^2 + (112t)^2} \;=\;\sqrt{16900t^2} \;=\;130t$ miles.

(a) When $\displaystyle t = 1\!:\;\;d \:=\:130(1) \:=\:130$ miles.

(b) At time $\displaystyle t$, their distance is: .$\displaystyle d \:=\:130t$ miles.

(c) If $\displaystyle d = 1300$, we have: .$\displaystyle 130t \:=\:1300 \quad\Rightarrow\quad t \:=\: 10$ hours.