After 40 minutes into a race, Cole has run ⁸₁₁ of the route while Xavier has covered only ²₁₁ of the distance. Cole runs at the same average speed throughout the race and Xavier’s average speed is 66 m/min slower than Cole’s. If Xavier wants to finish the race at the same time as Cole, by how many percent should he increase his average speed by for the remaining part of the race? Round off your answer to the nearest whole number.
Extra distance that Cole ran more than Xavier in first 40 min
= 40 x 66
= 2640 m

Fraction of the entire distance that was covered by Cole more than Xavier in the first 40 min
= ⁸₁₁ - ²₁₁
= ⁶₁₁

⁶₁₁ of the entire distance = 2640 m
¹₁₁ of the entire distance = 2640 ÷ 6 = 440 m

Distance that Xavier ran in the first 40 min
= 2 x 440
= 880 m

Xavier's average speed
= 880 ÷ 40
= 22 m/min

Cole's average speed
= 22 + 66
= 88 m/min

Fraction of the journey that Cole needed to run to complete the race
= 1 - ⁸₁₁
= ³₁₁

¹₁₁ of the entire distance = 440 m
³₁₁ of the entire distance = 3 x 440 = 1320 m

Duration that Cole would take to complete
= 1320 ÷ 88
= 15 min

Fraction of the journey that Cole needed to run to complete the race
= 1 - ²₁₁
= ⁹₁₁

⁹₁₁ of the entire distance = 9 x 440 = 3960 m  

Speed that Xavier needs to take to complete distance at the same time as Cole
= 3960 ÷ 15
= 264 m/min

Increase in Xavier's average speed
= 264 - 22
= 242 m/min

Percentage increase in Xavier's average speed
= ²⁴²₂₂ x 100%
≈ 1100%

Answer(s): 1100%