After 35 minutes into a race, Caden has run ⁵₁₁ of the route while Wesley has covered only ³₁₁ of the distance. Caden runs at the same average speed throughout the race and Wesley’s average speed is 102 m/min slower than Caden’s. If Wesley wants to finish the race at the same time as Caden, 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 Caden ran more than Wesley in first 35 min
= 35 x 102
= 3570 m

Fraction of the entire distance that was covered by Caden more than Wesley in the first 35 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 3570 m
¹₁₁ of the entire distance = 3570 ÷ 2 = 1785 m

Distance that Wesley ran in the first 35 min
= 3 x 1785
= 5355 m

Wesley's average speed
= 5355 ÷ 35
= 153 m/min

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

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

¹₁₁ of the entire distance = 1785 m
⁶₁₁ of the entire distance = 6 x 1785 = 10710 m

Duration that Caden would take to complete
= 10710 ÷ 255
= 42 min

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

⁸₁₁ of the entire distance = 8 x 1785 = 14280 m  

Speed that Wesley needs to take to complete distance at the same time as Caden
= 14280 ÷ 42
= 340 m/min

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

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

Answer(s): 122%