After 40 minutes into a race, Daniel has run ⁸₁₁ of the route while Perry has covered only ²₁₁ of the distance. Daniel runs at the same average speed throughout the race and Perry’s average speed is 69 m/min slower than Daniel’s. If Perry wants to finish the race at the same time as Daniel, 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 Daniel ran more than Perry in first 40 min
= 40 x 69
= 2760 m

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

⁶₁₁ of the entire distance = 2760 m
¹₁₁ of the entire distance = 2760 ÷ 6 = 460 m

Distance that Perry ran in the first 40 min
= 2 x 460
= 920 m

Perry's average speed
= 920 ÷ 40
= 23 m/min

Daniel's average speed
= 23 + 69
= 92 m/min

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

¹₁₁ of the entire distance = 460 m
³₁₁ of the entire distance = 3 x 460 = 1380 m

Duration that Daniel would take to complete
= 1380 ÷ 92
= 15 min

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

⁹₁₁ of the entire distance = 9 x 460 = 4140 m  

Speed that Perry needs to take to complete distance at the same time as Daniel
= 4140 ÷ 15
= 276 m/min

Increase in Perry's average speed
= 276 - 23
= 253 m/min

Percentage increase in Perry's average speed
= ²⁵³₂₃ x 100%
≈ 1100%

Answer(s): 1100%