After 40 minutes into a race, Peter has run ⁸₁₁ of the route while Xavier has covered only ²₁₁ of the distance. Peter runs at the same average speed throughout the race and Xavier’s average speed is 81 m/min slower than Peter’s. If Xavier wants to finish the race at the same time as Peter, 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 Peter ran more than Xavier in first 40 min
= 40 x 81
= 3240 m

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

⁶₁₁ of the entire distance = 3240 m
¹₁₁ of the entire distance = 3240 ÷ 6 = 540 m

Distance that Xavier ran in the first 40 min
= 2 x 540
= 1080 m

Xavier's average speed
= 1080 ÷ 40
= 27 m/min

Peter's average speed
= 27 + 81
= 108 m/min

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

¹₁₁ of the entire distance = 540 m
³₁₁ of the entire distance = 3 x 540 = 1620 m

Duration that Peter would take to complete
= 1620 ÷ 108
= 15 min

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

⁹₁₁ of the entire distance = 9 x 540 = 4860 m  

Speed that Xavier needs to take to complete distance at the same time as Peter
= 4860 ÷ 15
= 324 m/min

Increase in Xavier's average speed
= 324 - 27
= 297 m/min

Percentage increase in Xavier's average speed
= ²⁹⁷₂₇ x 100%
≈ 1100%

Answer(s): 1100%