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

Fraction of the entire distance that was covered by Bryan more than Vaidev 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 Vaidev ran in the first 40 min
= 2 x 640
= 1280 m

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

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

Fraction of the journey that Bryan 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 Bryan would take to complete
= 1920 ÷ 128
= 15 min

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

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

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

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

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

Answer(s): 1100%