Dean and Carlos decided to hold their own race. Dean estimates that he rides $3$ meters every $4$ seconds and wants a $5$-meter head start. Carlos will ride $1$ meter per second.  

1. How many meters does Dean ride each second?

   Hint (a):

   Use a proportion to solve the problem.

   Answer (a):

   $x = 0.75$

2. On one set of axes, graph and label lines to represent each rider's distance from the starting line. Find the equation for each rider.

   Hint (b):

   Write the equations for each rider based on the given information.
   Dean: $y = 0.75x + 5$
   Carlos: write a similar equation.

   

3. Use the equations you wrote to determine when Carlos and Dean will be the same distance from the starting line.

   Hint (c):

   Set the equations equal to each other and solve for $x$. Then substitute $x$ back into one
   of the original equations to solve for the distance from the starting line.