After 40 minutes into a race, Flynn has run ⁸₁₁ of the route while Ken has covered only ²₁₁ of the distance. Flynn runs at the same average speed throughout the race and Ken’s average speed is 108 m/min slower than Flynn’s. If Ken wants to finish the race at the same time as Flynn, 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 Flynn ran more than Ken in first 40 min
= 40 x 108
= 4320 m

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

⁶₁₁ of the entire distance = 4320 m
¹₁₁ of the entire distance = 4320 ÷ 6 = 720 m

Distance that Ken ran in the first 40 min
= 2 x 720
= 1440 m

Ken's average speed
= 1440 ÷ 40
= 36 m/min

Flynn's average speed
= 36 + 108
= 144 m/min

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

¹₁₁ of the entire distance = 720 m
³₁₁ of the entire distance = 3 x 720 = 2160 m

Duration that Flynn would take to complete
= 2160 ÷ 144
= 15 min

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

⁹₁₁ of the entire distance = 9 x 720 = 6480 m  

Speed that Ken needs to take to complete distance at the same time as Flynn
= 6480 ÷ 15
= 432 m/min

Increase in Ken's average speed
= 432 - 36
= 396 m/min

Percentage increase in Ken's average speed
= ³⁹⁶₃₆ x 100%
≈ 1100%

Answer(s): 1100%