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

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

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

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

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

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

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

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

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

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

Answer(s): 1100%