After 35 minutes into a race, Henry has run ⁷₁₃ of the route while Neave has covered only ⁴₁₃ of the distance. Henry runs at the same average speed throughout the race and Neave’s average speed is 102 m/min slower than Henry’s. If Neave 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 Neave in first 35 min
= 35 x 102
= 3570 m

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

³₁₃ of the entire distance = 3570 m
¹₁₃ of the entire distance = 3570 ÷ 3 = 1190 m

Distance that Neave ran in the first 35 min
= 4 x 1190
= 4760 m

Neave's average speed
= 4760 ÷ 35
= 136 m/min

Henry's average speed
= 136 + 102
= 238 m/min

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

¹₁₃ of the entire distance = 1190 m
⁶₁₃ of the entire distance = 6 x 1190 = 7140 m

Duration that Henry would take to complete
= 7140 ÷ 238
= 30 min

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

⁹₁₃ of the entire distance = 9 x 1190 = 10710 m  

Speed that Neave needs to take to complete distance at the same time as Henry
= 10710 ÷ 30
= 357 m/min

Increase in Neave's average speed
= 357 - 136
= 221 m/min

Percentage increase in Neave's average speed
= ²²¹₁₃₆ x 100%
≈ 163%

Answer(s): 163%