After 40 minutes into a race, Xavier has run ⁵₁₁ of the route while Mark has covered only ²₁₁ of the distance. Xavier runs at the same average speed throughout the race and Mark’s average speed is 54 m/min slower than Xavier’s. If Mark 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 Mark in first 40 min
= 40 x 54
= 2160 m

Fraction of the entire distance that was covered by Xavier more than Mark in the first 40 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 2160 m
¹₁₁ of the entire distance = 2160 ÷ 3 = 720 m

Distance that Mark ran in the first 40 min
= 2 x 720
= 1440 m

Mark's average speed
= 1440 ÷ 40
= 36 m/min

Xavier's average speed
= 36 + 54
= 90 m/min

Fraction of the journey that Xavier needed to run to complete the race
= 1 - ⁵₁₁
= ⁶₁₁

¹₁₁ of the entire distance = 720 m
⁶₁₁ of the entire distance = 6 x 720 = 4320 m

Duration that Xavier would take to complete
= 4320 ÷ 90
= 48 min

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

⁹₁₁ of the entire distance = 9 x 720 = 6480 m  

Speed that Mark needs to take to complete distance at the same time as Xavier
= 6480 ÷ 48
= 135 m/min

Increase in Mark's average speed
= 135 - 36
= 99 m/min

Percentage increase in Mark's average speed
= ⁹⁹₃₆ x 100%
≈ 275%

Answer(s): 275%