After 35 minutes into a race, Xavier has run ⁵₁₁ of the route while Lee has covered only ²₁₁ of the distance. Xavier runs at the same average speed throughout the race and Lee’s average speed is 108 m/min slower than Xavier’s. If Lee 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 Lee in first 35 min
= 35 x 108
= 3780 m

Fraction of the entire distance that was covered by Xavier more than Lee in the first 35 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 3780 m
¹₁₁ of the entire distance = 3780 ÷ 3 = 1260 m

Distance that Lee ran in the first 35 min
= 2 x 1260
= 2520 m

Lee's average speed
= 2520 ÷ 35
= 72 m/min

Xavier's average speed
= 72 + 108
= 180 m/min

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

¹₁₁ of the entire distance = 1260 m
⁶₁₁ of the entire distance = 6 x 1260 = 7560 m

Duration that Xavier would take to complete
= 7560 ÷ 180
= 42 min

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

⁹₁₁ of the entire distance = 9 x 1260 = 11340 m  

Speed that Lee needs to take to complete distance at the same time as Xavier
= 11340 ÷ 42
= 270 m/min

Increase in Lee's average speed
= 270 - 72
= 198 m/min

Percentage increase in Lee's average speed
= ¹⁹⁸₇₂ x 100%
≈ 275%

Answer(s): 275%