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

Fraction of the entire distance that was covered by Justin more than Caden 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 Caden ran in the first 40 min
= 2 x 460
= 920 m

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

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

Fraction of the journey that Justin 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 Justin would take to complete
= 1380 ÷ 92
= 15 min

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

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

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

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

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

Answer(s): 1100%