After 40 minutes into a race, Sean has run ⁸₁₁ of the route while Seth has covered only ²₁₁ of the distance. Sean runs at the same average speed throughout the race and Seth’s average speed is 96 m/min slower than Sean’s. If Seth wants to finish the race at the same time as Sean, 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 Sean ran more than Seth in first 40 min
= 40 x 96
= 3840 m

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

⁶₁₁ of the entire distance = 3840 m
¹₁₁ of the entire distance = 3840 ÷ 6 = 640 m

Distance that Seth ran in the first 40 min
= 2 x 640
= 1280 m

Seth's average speed
= 1280 ÷ 40
= 32 m/min

Sean's average speed
= 32 + 96
= 128 m/min

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

¹₁₁ of the entire distance = 640 m
³₁₁ of the entire distance = 3 x 640 = 1920 m

Duration that Sean would take to complete
= 1920 ÷ 128
= 15 min

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

⁹₁₁ of the entire distance = 9 x 640 = 5760 m  

Speed that Seth needs to take to complete distance at the same time as Sean
= 5760 ÷ 15
= 384 m/min

Increase in Seth's average speed
= 384 - 32
= 352 m/min

Percentage increase in Seth's average speed
= ³⁵²₃₂ x 100%
≈ 1100%

Answer(s): 1100%