After 40 minutes into a race, Oscar has run ⁸₁₁ of the route while Ivan has covered only ²₁₁ of the distance. Oscar runs at the same average speed throughout the race and Ivan’s average speed is 45 m/min slower than Oscar’s. If Ivan wants to finish the race at the same time as Oscar, 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 Oscar ran more than Ivan in first 40 min
= 40 x 45
= 1800 m

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

⁶₁₁ of the entire distance = 1800 m
¹₁₁ of the entire distance = 1800 ÷ 6 = 300 m

Distance that Ivan ran in the first 40 min
= 2 x 300
= 600 m

Ivan's average speed
= 600 ÷ 40
= 15 m/min

Oscar's average speed
= 15 + 45
= 60 m/min

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

¹₁₁ of the entire distance = 300 m
³₁₁ of the entire distance = 3 x 300 = 900 m

Duration that Oscar would take to complete
= 900 ÷ 60
= 15 min

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

⁹₁₁ of the entire distance = 9 x 300 = 2700 m  

Speed that Ivan needs to take to complete distance at the same time as Oscar
= 2700 ÷ 15
= 180 m/min

Increase in Ivan's average speed
= 180 - 15
= 165 m/min

Percentage increase in Ivan's average speed
= ¹⁶⁵₁₅ x 100%
≈ 1100%

Answer(s): 1100%