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

Fraction of the entire distance that was covered by Fabian more than Oliver 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 Oliver ran in the first 40 min
= 2 x 560
= 1120 m

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

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

Fraction of the journey that Fabian 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 Fabian would take to complete
= 1680 ÷ 112
= 15 min

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

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

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

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

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

Answer(s): 1100%