After 40 minutes into a race, Vincent has run ⁸₁₁ of the route while Fabian has covered only ²₁₁ of the distance. Vincent runs at the same average speed throughout the race and Fabian’s average speed is 84 m/min slower than Vincent’s. If Fabian wants to finish the race at the same time as Vincent, 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 Vincent ran more than Fabian in first 40 min
= 40 x 84
= 3360 m

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

⁶₁₁ of the entire distance = 3360 m
¹₁₁ of the entire distance = 3360 ÷ 6 = 560 m

Distance that Fabian ran in the first 40 min
= 2 x 560
= 1120 m

Fabian's average speed
= 1120 ÷ 40
= 28 m/min

Vincent's average speed
= 28 + 84
= 112 m/min

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

¹₁₁ of the entire distance = 560 m
³₁₁ of the entire distance = 3 x 560 = 1680 m

Duration that Vincent would take to complete
= 1680 ÷ 112
= 15 min

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

⁹₁₁ of the entire distance = 9 x 560 = 5040 m  

Speed that Fabian needs to take to complete distance at the same time as Vincent
= 5040 ÷ 15
= 336 m/min

Increase in Fabian's average speed
= 336 - 28
= 308 m/min

Percentage increase in Fabian's average speed
= ³⁰⁸₂₈ x 100%
≈ 1100%

Answer(s): 1100%