After 40 minutes into a race, Asher has run ⁸₁₁ of the route while Jenson has covered only ²₁₁ of the distance. Asher runs at the same average speed throughout the race and Jenson’s average speed is 69 m/min slower than Asher’s. If Jenson wants to finish the race at the same time as Asher, 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 Asher ran more than Jenson in first 40 min
= 40 x 69
= 2760 m

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

⁶₁₁ of the entire distance = 2760 m
¹₁₁ of the entire distance = 2760 ÷ 6 = 460 m

Distance that Jenson ran in the first 40 min
= 2 x 460
= 920 m

Jenson's average speed
= 920 ÷ 40
= 23 m/min

Asher's average speed
= 23 + 69
= 92 m/min

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

¹₁₁ of the entire distance = 460 m
³₁₁ of the entire distance = 3 x 460 = 1380 m

Duration that Asher would take to complete
= 1380 ÷ 92
= 15 min

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

⁹₁₁ of the entire distance = 9 x 460 = 4140 m  

Speed that Jenson needs to take to complete distance at the same time as Asher
= 4140 ÷ 15
= 276 m/min

Increase in Jenson's average speed
= 276 - 23
= 253 m/min

Percentage increase in Jenson's average speed
= ²⁵³₂₃ x 100%
≈ 1100%

Answer(s): 1100%