After 40 minutes into a race, Luis has run ⁸₁₁ of the route while Glen has covered only ²₁₁ of the distance. Luis runs at the same average speed throughout the race and Glen’s average speed is 93 m/min slower than Luis’s. If Glen wants to finish the race at the same time as Luis, 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 Luis ran more than Glen in first 40 min
= 40 x 93
= 3720 m

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

⁶₁₁ of the entire distance = 3720 m
¹₁₁ of the entire distance = 3720 ÷ 6 = 620 m

Distance that Glen ran in the first 40 min
= 2 x 620
= 1240 m

Glen's average speed
= 1240 ÷ 40
= 31 m/min

Luis's average speed
= 31 + 93
= 124 m/min

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

¹₁₁ of the entire distance = 620 m
³₁₁ of the entire distance = 3 x 620 = 1860 m

Duration that Luis would take to complete
= 1860 ÷ 124
= 15 min

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

⁹₁₁ of the entire distance = 9 x 620 = 5580 m  

Speed that Glen needs to take to complete distance at the same time as Luis
= 5580 ÷ 15
= 372 m/min

Increase in Glen's average speed
= 372 - 31
= 341 m/min

Percentage increase in Glen's average speed
= ³⁴¹₃₁ x 100%
≈ 1100%

Answer(s): 1100%