After 40 minutes into a race, Ryan has run ⁸₁₁ of the route while Fred has covered only ²₁₁ of the distance. Ryan runs at the same average speed throughout the race and Fred’s average speed is 81 m/min slower than Ryan’s. If Fred wants to finish the race at the same time as Ryan, 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 Ryan ran more than Fred in first 40 min
= 40 x 81
= 3240 m

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

⁶₁₁ of the entire distance = 3240 m
¹₁₁ of the entire distance = 3240 ÷ 6 = 540 m

Distance that Fred ran in the first 40 min
= 2 x 540
= 1080 m

Fred's average speed
= 1080 ÷ 40
= 27 m/min

Ryan's average speed
= 27 + 81
= 108 m/min

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

¹₁₁ of the entire distance = 540 m
³₁₁ of the entire distance = 3 x 540 = 1620 m

Duration that Ryan would take to complete
= 1620 ÷ 108
= 15 min

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

⁹₁₁ of the entire distance = 9 x 540 = 4860 m  

Speed that Fred needs to take to complete distance at the same time as Ryan
= 4860 ÷ 15
= 324 m/min

Increase in Fred's average speed
= 324 - 27
= 297 m/min

Percentage increase in Fred's average speed
= ²⁹⁷₂₇ x 100%
≈ 1100%

Answer(s): 1100%