After 30 minutes into a race, Henry has run ⁵₁₁ of the route while Flynn has covered only ³₁₁ of the distance. Henry runs at the same average speed throughout the race and Flynn’s average speed is 102 m/min slower than Henry’s. If Flynn wants to finish the race at the same time as Henry, 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 Henry ran more than Flynn in first 30 min
= 30 x 102
= 3060 m

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

²₁₁ of the entire distance = 3060 m
¹₁₁ of the entire distance = 3060 ÷ 2 = 1530 m

Distance that Flynn ran in the first 30 min
= 3 x 1530
= 4590 m

Flynn's average speed
= 4590 ÷ 30
= 153 m/min

Henry's average speed
= 153 + 102
= 255 m/min

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

¹₁₁ of the entire distance = 1530 m
⁶₁₁ of the entire distance = 6 x 1530 = 9180 m

Duration that Henry would take to complete
= 9180 ÷ 255
= 36 min

Fraction of the journey that Henry needed to run to complete the race
= 1 - ³₁₁
= ⁸₁₁

⁸₁₁ of the entire distance = 8 x 1530 = 12240 m  

Speed that Flynn needs to take to complete distance at the same time as Henry
= 12240 ÷ 36
= 340 m/min

Increase in Flynn's average speed
= 340 - 153
= 187 m/min

Percentage increase in Flynn's average speed
= ¹⁸⁷₁₅₃ x 100%
≈ 122%

Answer(s): 122%