After 25 minutes into a race, Julian has run ⁵₁₁ of the route while Luis has covered only ²₁₁ of the distance. Julian runs at the same average speed throughout the race and Luis’s average speed is 66 m/min slower than Julian’s. If Luis wants to finish the race at the same time as Julian, 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 Julian ran more than Luis in first 25 min
= 25 x 66
= 1650 m

Fraction of the entire distance that was covered by Julian more than Luis in the first 25 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 1650 m
¹₁₁ of the entire distance = 1650 ÷ 3 = 550 m

Distance that Luis ran in the first 25 min
= 2 x 550
= 1100 m

Luis's average speed
= 1100 ÷ 25
= 44 m/min

Julian's average speed
= 44 + 66
= 110 m/min

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

¹₁₁ of the entire distance = 550 m
⁶₁₁ of the entire distance = 6 x 550 = 3300 m

Duration that Julian would take to complete
= 3300 ÷ 110
= 30 min

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

⁹₁₁ of the entire distance = 9 x 550 = 4950 m  

Speed that Luis needs to take to complete distance at the same time as Julian
= 4950 ÷ 30
= 165 m/min

Increase in Luis's average speed
= 165 - 44
= 121 m/min

Percentage increase in Luis's average speed
= ¹²¹₄₄ x 100%
≈ 275%

Answer(s): 275%