After 40 minutes into a race, Pierre has run ⁸₁₁ of the route while Charlie has covered only ²₁₁ of the distance. Pierre runs at the same average speed throughout the race and Charlie’s average speed is 54 m/min slower than Pierre’s. If Charlie wants to finish the race at the same time as Pierre, 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 Pierre ran more than Charlie in first 40 min
= 40 x 54
= 2160 m

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

⁶₁₁ of the entire distance = 2160 m
¹₁₁ of the entire distance = 2160 ÷ 6 = 360 m

Distance that Charlie ran in the first 40 min
= 2 x 360
= 720 m

Charlie's average speed
= 720 ÷ 40
= 18 m/min

Pierre's average speed
= 18 + 54
= 72 m/min

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

¹₁₁ of the entire distance = 360 m
³₁₁ of the entire distance = 3 x 360 = 1080 m

Duration that Pierre would take to complete
= 1080 ÷ 72
= 15 min

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

⁹₁₁ of the entire distance = 9 x 360 = 3240 m  

Speed that Charlie needs to take to complete distance at the same time as Pierre
= 3240 ÷ 15
= 216 m/min

Increase in Charlie's average speed
= 216 - 18
= 198 m/min

Percentage increase in Charlie's average speed
= ¹⁹⁸₁₈ x 100%
≈ 1100%

Answer(s): 1100%