In a bicycle race, bicyclists rode $82$ miles on the first day. The $82$ miles represented $20\%$ of the entire race.

1. How long was the entire bicycle race? Write an equation and then use it to find your answer. Remember to define your variable.

   Hint (a):

   Create a table to represent the race.
   We know that the bicyclists rode $82$ miles or $20\%$ of the race.
   The rest of the race is $80\%$ since: $100\%$ (total) $- 20\%$ (first day) $= 80\%$ (rest of the race)

   More Help (a):

   -The bicyclists rode $82$ miles which was $20\%$ of the entire race.
   -Let $r$ represent the total race length.
   Set up an equation and solve: $82 = 0.2r$

    

   $\begin{array}{|c|c|c|} \hline \textbf{Section} & \textbf{Distance} & \textbf{Percent}\\ \hline \text{A} & 82 & 20\% \\ \hline \text{B} & \text{unknown} & 80\% \\ \hline \end{array}$

   Answer (a):

   The total length of the race is $410$ miles.

2. If bicyclists rode $21\%$ of the race on the second day, how many miles did they ride on the second day?

   Hint (b):

   We already know that the entire race is $410$ miles.
   On the second day, they rode $21\%$ of the entire $410$ miles.
   Set up an equation and solve:
   $\left(0.21\right)\left(410\right) = x$ (Let $x$ represent the miles for the second day)

3. After completing the first two days as described in parts (a) and (b), the bicyclists have what percentage of the race left to ride?

   Hint (c):

   The bicyclists rode $20\%$ the first day and $21\%$ the second day.

   Step 1 (c):

   Add $20\%$ and $21\%$ to find the total percent the bicyclists rode the first two days.

   Step 2 (c):

   Subtract the total percent for the first two days from $100\%$ (Percent of the entire race).

4. How many miles do the bicyclists have left to ride?

   Hint (d):

   Add the distance the bicyclists rode on day $2$ of the race (answer to part (b)) to the distance they rode on day $1$ ($82$ miles) and subtract this from the total distance of the race (answer from part (a)).

   Answer (d):

   The bicyclists have $241.9$ miles left to ride.