After 35 minutes into a race, Flynn has run ⁷₁₃ of the route while Julian has covered only ⁴₁₃ of the distance. Flynn runs at the same average speed throughout the race and Julian’s average speed is 30 m/min slower than Flynn’s. If Julian wants to finish the race at the same time as Flynn, 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 Flynn ran more than Julian in first 35 min
= 35 x 30
= 1050 m

Fraction of the entire distance that was covered by Flynn more than Julian in the first 35 min
= ⁷₁₃ - ⁴₁₃
= ³₁₃

³₁₃ of the entire distance = 1050 m
¹₁₃ of the entire distance = 1050 ÷ 3 = 350 m

Distance that Julian ran in the first 35 min
= 4 x 350
= 1400 m

Julian's average speed
= 1400 ÷ 35
= 40 m/min

Flynn's average speed
= 40 + 30
= 70 m/min

Fraction of the journey that Flynn needed to run to complete the race
= 1 - ⁷₁₃
= ⁶₁₃

¹₁₃ of the entire distance = 350 m
⁶₁₃ of the entire distance = 6 x 350 = 2100 m

Duration that Flynn would take to complete
= 2100 ÷ 70
= 30 min

Fraction of the journey that Flynn needed to run to complete the race
= 1 - ⁴₁₃
= ⁹₁₃

⁹₁₃ of the entire distance = 9 x 350 = 3150 m  

Speed that Julian needs to take to complete distance at the same time as Flynn
= 3150 ÷ 30
= 105 m/min

Increase in Julian's average speed
= 105 - 40
= 65 m/min

Percentage increase in Julian's average speed
= ⁶⁵₄₀ x 100%
≈ 163%

Answer(s): 163%