After 40 minutes into a race, Xavier has run ⁸₁₁ of the route while Liam has covered only ²₁₁ of the distance. Xavier runs at the same average speed throughout the race and Liam’s average speed is 72 m/min slower than Xavier’s. If Liam wants to finish the race at the same time as Xavier, 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 Xavier ran more than Liam in first 40 min
= 40 x 72
= 2880 m

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

⁶₁₁ of the entire distance = 2880 m
¹₁₁ of the entire distance = 2880 ÷ 6 = 480 m

Distance that Liam ran in the first 40 min
= 2 x 480
= 960 m

Liam's average speed
= 960 ÷ 40
= 24 m/min

Xavier's average speed
= 24 + 72
= 96 m/min

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

¹₁₁ of the entire distance = 480 m
³₁₁ of the entire distance = 3 x 480 = 1440 m

Duration that Xavier would take to complete
= 1440 ÷ 96
= 15 min

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

⁹₁₁ of the entire distance = 9 x 480 = 4320 m  

Speed that Liam needs to take to complete distance at the same time as Xavier
= 4320 ÷ 15
= 288 m/min

Increase in Liam's average speed
= 288 - 24
= 264 m/min

Percentage increase in Liam's average speed
= ²⁶⁴₂₄ x 100%
≈ 1100%

Answer(s): 1100%