​How are distance, rate, and time related? 

1. Suppose you are driving at a steady rate of $20$ mph. How long will it take you to travel $80$ miles?

   Step (a):

   $80\ \text{ miles }\cdot\ \frac{1\ \text { hour }}{20\ \text { miles }}$

2. Now suppose you are driving at a steady rate of $60$ mph, so three times as fast. Now how long will it take you to travel $80$ miles?

   Step (b):

   $80\ \text{ miles }\cdot\ \frac{1\ \text { hour }}{60\ \text { miles }}$

3. If you are driving at $r$ mph, write an expression for the time it takes to drive $d$ miles.

   Hint (c):

   $\text{If }d=rt\text{, then }t=?$

4. If you increase your speed by a multiple of $m$, write an expression for the time it takes to drive $d$ miles.

   Hint (d):

   Your rate is now $r·m$.