In a $412$-mile bicycle race, bicyclists complete $20\%$ on the first day.

1. How far do they ride on this day? Show how you get your answer.

   Hint (a):

   $10\%$ of the race is $41.2$ miles. Why does this make sense? How could you use that to calculate $20\%$ of the race?

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

   Hint (b):

   How could you find the length of $1\%$ of the race? Can you combine that with your answer from part (a) to find $21\%$ of the race?

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

   Hint (c):

   They have ridden $20\% + 21\% = 41\%$ of the race. What percentage is left?

4. How many miles do they have left to ride?

   Hint (d):

   You can do this by calculating another percentage of the race.
   Or you can do it by subtracting the miles they have already ridden from the total length of the race.
   Which method do you prefer?
   You can try doing both to check that they get the same answer!