After 30 minutes into a race, Flynn has run ⁶₁₃ of the route while Harry has covered only ⁴₁₃ of the distance. Flynn runs at the same average speed throughout the race and Harry’s average speed is 63 m/min slower than Flynn’s. If Harry 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 Harry in first 30 min
= 30 x 63
= 1890 m

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

²₁₃ of the entire distance = 1890 m
¹₁₃ of the entire distance = 1890 ÷ 2 = 945 m

Distance that Harry ran in the first 30 min
= 4 x 945
= 3780 m

Harry's average speed
= 3780 ÷ 30
= 126 m/min

Flynn's average speed
= 126 + 63
= 189 m/min

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

¹₁₃ of the entire distance = 945 m
⁷₁₃ of the entire distance = 7 x 945 = 6615 m

Duration that Flynn would take to complete
= 6615 ÷ 189
= 35 min

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

⁹₁₃ of the entire distance = 9 x 945 = 8505 m  

Speed that Harry needs to take to complete distance at the same time as Flynn
= 8505 ÷ 35
= 243 m/min

Increase in Harry's average speed
= 243 - 126
= 117 m/min

Percentage increase in Harry's average speed
= ¹¹⁷₁₂₆ x 100%
≈ 93%

Answer(s): 93%