After 40 minutes into a race, Vaidev has run ⁸₁₁ of the route while Harry has covered only ²₁₁ of the distance. Vaidev runs at the same average speed throughout the race and Harry’s average speed is 81 m/min slower than Vaidev’s. If Harry wants to finish the race at the same time as Vaidev, 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 Vaidev ran more than Harry in first 40 min
= 40 x 81
= 3240 m

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

⁶₁₁ of the entire distance = 3240 m
¹₁₁ of the entire distance = 3240 ÷ 6 = 540 m

Distance that Harry ran in the first 40 min
= 2 x 540
= 1080 m

Harry's average speed
= 1080 ÷ 40
= 27 m/min

Vaidev's average speed
= 27 + 81
= 108 m/min

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

¹₁₁ of the entire distance = 540 m
³₁₁ of the entire distance = 3 x 540 = 1620 m

Duration that Vaidev would take to complete
= 1620 ÷ 108
= 15 min

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

⁹₁₁ of the entire distance = 9 x 540 = 4860 m  

Speed that Harry needs to take to complete distance at the same time as Vaidev
= 4860 ÷ 15
= 324 m/min

Increase in Harry's average speed
= 324 - 27
= 297 m/min

Percentage increase in Harry's average speed
= ²⁹⁷₂₇ x 100%
≈ 1100%

Answer(s): 1100%