After 30 minutes into a race, Riordan has run ⁵₁₁ of the route while Julian has covered only ²₁₁ of the distance. Riordan runs at the same average speed throughout the race and Julian’s average speed is 120 m/min slower than Riordan’s. If Julian wants to finish the race at the same time as Riordan, 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 Riordan ran more than Julian in first 30 min
= 30 x 120
= 3600 m

Fraction of the entire distance that was covered by Riordan more than Julian in the first 30 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 3600 m
¹₁₁ of the entire distance = 3600 ÷ 3 = 1200 m

Distance that Julian ran in the first 30 min
= 2 x 1200
= 2400 m

Julian's average speed
= 2400 ÷ 30
= 80 m/min

Riordan's average speed
= 80 + 120
= 200 m/min

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

¹₁₁ of the entire distance = 1200 m
⁶₁₁ of the entire distance = 6 x 1200 = 7200 m

Duration that Riordan would take to complete
= 7200 ÷ 200
= 36 min

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

⁹₁₁ of the entire distance = 9 x 1200 = 10800 m  

Speed that Julian needs to take to complete distance at the same time as Riordan
= 10800 ÷ 36
= 300 m/min

Increase in Julian's average speed
= 300 - 80
= 220 m/min

Percentage increase in Julian's average speed
= ²²⁰₈₀ x 100%
≈ 275%

Answer(s): 275%