After 40 minutes into a race, Valen has run ⁸₁₁ of the route while Ben has covered only ²₁₁ of the distance. Valen runs at the same average speed throughout the race and Ben’s average speed is 33 m/min slower than Valen’s. If Ben wants to finish the race at the same time as Valen, 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 Valen ran more than Ben in first 40 min
= 40 x 33
= 1320 m

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

⁶₁₁ of the entire distance = 1320 m
¹₁₁ of the entire distance = 1320 ÷ 6 = 220 m

Distance that Ben ran in the first 40 min
= 2 x 220
= 440 m

Ben's average speed
= 440 ÷ 40
= 11 m/min

Valen's average speed
= 11 + 33
= 44 m/min

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

¹₁₁ of the entire distance = 220 m
³₁₁ of the entire distance = 3 x 220 = 660 m

Duration that Valen would take to complete
= 660 ÷ 44
= 15 min

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

⁹₁₁ of the entire distance = 9 x 220 = 1980 m  

Speed that Ben needs to take to complete distance at the same time as Valen
= 1980 ÷ 15
= 132 m/min

Increase in Ben's average speed
= 132 - 11
= 121 m/min

Percentage increase in Ben's average speed
= ¹²¹₁₁ x 100%
≈ 1100%

Answer(s): 1100%