After 40 minutes into a race, Ian has run ⁸₁₁ of the route while Fred has covered only ²₁₁ of the distance. Ian runs at the same average speed throughout the race and Fred’s average speed is 72 m/min slower than Ian’s. If Fred wants to finish the race at the same time as Ian, 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 Ian ran more than Fred in first 40 min
= 40 x 72
= 2880 m

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

⁶₁₁ of the entire distance = 2880 m
¹₁₁ of the entire distance = 2880 ÷ 6 = 480 m

Distance that Fred ran in the first 40 min
= 2 x 480
= 960 m

Fred's average speed
= 960 ÷ 40
= 24 m/min

Ian's average speed
= 24 + 72
= 96 m/min

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

¹₁₁ of the entire distance = 480 m
³₁₁ of the entire distance = 3 x 480 = 1440 m

Duration that Ian would take to complete
= 1440 ÷ 96
= 15 min

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

⁹₁₁ of the entire distance = 9 x 480 = 4320 m  

Speed that Fred needs to take to complete distance at the same time as Ian
= 4320 ÷ 15
= 288 m/min

Increase in Fred's average speed
= 288 - 24
= 264 m/min

Percentage increase in Fred's average speed
= ²⁶⁴₂₄ x 100%
≈ 1100%

Answer(s): 1100%