Answer
a) Speed skater B won the race.
b) Skater A had an average speed of $20 {m\over s}$ while skater B had an average speed of $10 {m\over s}$
c) Skater A had an average speed of ${20\over3} {m\over s}$ while skater B had an average speed of $20 {m\over s}$
Work Step by Step
a) Skater A reached the $500$ m value in less time than skater B.
b) To find the average speed, we'll use the formula $v_{avg}={f(b)-f(a) \over b-a}$
So, during the first ten seconds, $a=0$ and $b=10$.
Skater A: $v_{avg}={200-0 \over 10-0}{m\over s} = 20{m\over s}$
Skater B: $v_{avg}={100-0 \over 10-0}{m\over s} = 10{m\over s}$
c) We'll use the same formula, but the values for each skater are different:
Skater A: $v_{avg}={f(40)-f(25) \over 40-25} ={500-400 \over 15}{m\over s} ={100 \over 15}{m\over s}={20\over3}{m\over s}$
Skater B: $v_{avg}={f(35)-f(20) \over 35-20} ={500-200 \over 15}{m\over s} ={300 \over 15}{m\over s}={20}{m\over s}$
