After 40 minutes into a race, Simon has run ⁸₁₁ of the route while Ethan has covered only ²₁₁ of the distance. Simon runs at the same average speed throughout the race and Ethan’s average speed is 66 m/min slower than Simon’s. If Ethan wants to finish the race at the same time as Simon, 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 Simon ran more than Ethan in first 40 min
= 40 x 66
= 2640 m

Fraction of the entire distance that was covered by Simon more than Ethan 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 Ethan ran in the first 40 min
= 2 x 440
= 880 m

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

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

Fraction of the journey that Simon 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 Simon would take to complete
= 1320 ÷ 88
= 15 min

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

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

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

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

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

Answer(s): 1100%