After 40 minutes into a race, Wesley has run ⁸₁₁ of the route while Vincent has covered only ²₁₁ of the distance. Wesley runs at the same average speed throughout the race and Vincent’s average speed is 120 m/min slower than Wesley’s. If Vincent wants to finish the race at the same time as Wesley, 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 Wesley ran more than Vincent in first 40 min
= 40 x 120
= 4800 m

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

⁶₁₁ of the entire distance = 4800 m
¹₁₁ of the entire distance = 4800 ÷ 6 = 800 m

Distance that Vincent ran in the first 40 min
= 2 x 800
= 1600 m

Vincent's average speed
= 1600 ÷ 40
= 40 m/min

Wesley's average speed
= 40 + 120
= 160 m/min

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

¹₁₁ of the entire distance = 800 m
³₁₁ of the entire distance = 3 x 800 = 2400 m

Duration that Wesley would take to complete
= 2400 ÷ 160
= 15 min

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

⁹₁₁ of the entire distance = 9 x 800 = 7200 m  

Speed that Vincent needs to take to complete distance at the same time as Wesley
= 7200 ÷ 15
= 480 m/min

Increase in Vincent's average speed
= 480 - 40
= 440 m/min

Percentage increase in Vincent's average speed
= ⁴⁴⁰₄₀ x 100%
≈ 1100%

Answer(s): 1100%