After 25 minutes into a race, Fabian has run ⁵₁₁ of the route while Cody has covered only ³₁₁ of the distance. Fabian runs at the same average speed throughout the race and Cody’s average speed is 120 m/min slower than Fabian’s. If Cody wants to finish the race at the same time as Fabian, 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 Fabian ran more than Cody in first 25 min
= 25 x 120
= 3000 m

Fraction of the entire distance that was covered by Fabian more than Cody in the first 25 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 3000 m
¹₁₁ of the entire distance = 3000 ÷ 2 = 1500 m

Distance that Cody ran in the first 25 min
= 3 x 1500
= 4500 m

Cody's average speed
= 4500 ÷ 25
= 180 m/min

Fabian's average speed
= 180 + 120
= 300 m/min

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

¹₁₁ of the entire distance = 1500 m
⁶₁₁ of the entire distance = 6 x 1500 = 9000 m

Duration that Fabian would take to complete
= 9000 ÷ 300
= 30 min

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

⁸₁₁ of the entire distance = 8 x 1500 = 12000 m  

Speed that Cody needs to take to complete distance at the same time as Fabian
= 12000 ÷ 30
= 400 m/min

Increase in Cody's average speed
= 400 - 180
= 220 m/min

Percentage increase in Cody's average speed
= ²²⁰₁₈₀ x 100%
≈ 122%

Answer(s): 122%