After 35 minutes into a race, Elijah has run ⁷₁₃ of the route while Seth has covered only ⁴₁₃ of the distance. Elijah runs at the same average speed throughout the race and Seth’s average speed is 102 m/min slower than Elijah’s. If Seth wants to finish the race at the same time as Elijah, 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 Elijah ran more than Seth in first 35 min
= 35 x 102
= 3570 m

Fraction of the entire distance that was covered by Elijah more than Seth 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 Seth ran in the first 35 min
= 4 x 1190
= 4760 m

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

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

Fraction of the journey that Elijah 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 Elijah would take to complete
= 7140 ÷ 238
= 30 min

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

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

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

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

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

Answer(s): 163%