Mike has two toy boats. The first travels at a constant rate of $10$ ft/sec. The second accelerates so that it has a rate of $t$ ft/sec.

1. Sketch speed vs. time graphs for each boat.

   Hint (a):

   Put time on the $x$-axis and speed (or rate) on the $y$-axis.

2. How far has each boat traveled after $5$ seconds?

   Hint (b):

   Distance = (rate)(time), or using your graph
   it is the area under the curve.

3. How far will they have traveled after $t$ seconds?

   Answer (c):

   First boat: $d = 5\left(t\right)$
   Second boat: $d = 0.5\left(t\right)\left(t\right)$

4. When will the second boat pass the first?

   Hint (d):

   When $5t = 0.5t^2$.