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

Fraction of the entire distance that was covered by Julian more than Gabriel 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 Gabriel ran in the first 40 min
= 2 x 720
= 1440 m

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

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

Fraction of the journey that Julian 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 Julian would take to complete
= 2160 ÷ 144
= 15 min

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

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

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

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

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

Answer(s): 1100%