After 40 minutes into a race, Neave has run ⁸₁₁ of the route while Ben has covered only ²₁₁ of the distance. Neave runs at the same average speed throughout the race and Ben’s average speed is 99 m/min slower than Neave’s. If Ben wants to finish the race at the same time as Neave, 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 Neave ran more than Ben in first 40 min
= 40 x 99
= 3960 m

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

⁶₁₁ of the entire distance = 3960 m
¹₁₁ of the entire distance = 3960 ÷ 6 = 660 m

Distance that Ben ran in the first 40 min
= 2 x 660
= 1320 m

Ben's average speed
= 1320 ÷ 40
= 33 m/min

Neave's average speed
= 33 + 99
= 132 m/min

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

¹₁₁ of the entire distance = 660 m
³₁₁ of the entire distance = 3 x 660 = 1980 m

Duration that Neave would take to complete
= 1980 ÷ 132
= 15 min

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

⁹₁₁ of the entire distance = 9 x 660 = 5940 m  

Speed that Ben needs to take to complete distance at the same time as Neave
= 5940 ÷ 15
= 396 m/min

Increase in Ben's average speed
= 396 - 33
= 363 m/min

Percentage increase in Ben's average speed
= ³⁶³₃₃ x 100%
≈ 1100%

Answer(s): 1100%