At noon, John is $60$ miles directly south of Cactus Junction and driving north at $40$ miles per hour. At the same time, Amy is $20$ miles west of Cactus Junction and driving east at $30$ miles per hour. 

1. Express the distance of John’s car north of Cactus Junction as a function of time.

   Hint (a):

   How far away is John from Cactus Junction now?
   A position north of Cactus Junction should be positive, so what value would a position south of Cactus Junction be

   What expression describes his distance?

2. Express the distance of Amy’s car east of Cactus Junction as a function of time.

   Hint (b):

   Follow the example for John's distance.

3. Find the distance between John and Amy at the time $t$ hours after noon.

   Hint (c):

   Use the distance formula.

4. When are John and Amy’s cars closest together? (Hint: Graph the distance equation you found in part (c).)