After 35 minutes into a race, Rael has run ⁵₁₁ of the route while Cody has covered only ³₁₁ of the distance. Rael runs at the same average speed throughout the race and Cody’s average speed is 90 m/min slower than Rael’s. If Cody wants to finish the race at the same time as Rael, 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 Rael ran more than Cody in first 35 min
= 35 x 90
= 3150 m

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

²₁₁ of the entire distance = 3150 m
¹₁₁ of the entire distance = 3150 ÷ 2 = 1575 m

Distance that Cody ran in the first 35 min
= 3 x 1575
= 4725 m

Cody's average speed
= 4725 ÷ 35
= 135 m/min

Rael's average speed
= 135 + 90
= 225 m/min

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

¹₁₁ of the entire distance = 1575 m
⁶₁₁ of the entire distance = 6 x 1575 = 9450 m

Duration that Rael would take to complete
= 9450 ÷ 225
= 42 min

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

⁸₁₁ of the entire distance = 8 x 1575 = 12600 m  

Speed that Cody needs to take to complete distance at the same time as Rael
= 12600 ÷ 42
= 300 m/min

Increase in Cody's average speed
= 300 - 135
= 165 m/min

Percentage increase in Cody's average speed
= ¹⁶⁵₁₃₅ x 100%
≈ 122%

Answer(s): 122%