After 30 minutes into a race, Perry has run ⁶₁₃ of the route while Flynn has covered only ⁴₁₃ of the distance. Perry runs at the same average speed throughout the race and Flynn’s average speed is 91 m/min slower than Perry’s. If Flynn wants to finish the race at the same time as Perry, 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 Perry ran more than Flynn in first 30 min
= 30 x 91
= 2730 m

Fraction of the entire distance that was covered by Perry more than Flynn in the first 30 min
= ⁶₁₃ - ⁴₁₃
= ²₁₃

²₁₃ of the entire distance = 2730 m
¹₁₃ of the entire distance = 2730 ÷ 2 = 1365 m

Distance that Flynn ran in the first 30 min
= 4 x 1365
= 5460 m

Flynn's average speed
= 5460 ÷ 30
= 182 m/min

Perry's average speed
= 182 + 91
= 273 m/min

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

¹₁₃ of the entire distance = 1365 m
⁷₁₃ of the entire distance = 7 x 1365 = 9555 m

Duration that Perry would take to complete
= 9555 ÷ 273
= 35 min

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

⁹₁₃ of the entire distance = 9 x 1365 = 12285 m  

Speed that Flynn needs to take to complete distance at the same time as Perry
= 12285 ÷ 35
= 351 m/min

Increase in Flynn's average speed
= 351 - 182
= 169 m/min

Percentage increase in Flynn's average speed
= ¹⁶⁹₁₈₂ x 100%
≈ 93%

Answer(s): 93%