After 30 minutes into a race, Cody has run ⁵₁₁ of the route while Billy has covered only ³₁₁ of the distance. Cody runs at the same average speed throughout the race and Billy’s average speed is 108 m/min slower than Cody’s. If Billy wants to finish the race at the same time as Cody, 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 Cody ran more than Billy in first 30 min
= 30 x 108
= 3240 m

Fraction of the entire distance that was covered by Cody more than Billy in the first 30 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 3240 m
¹₁₁ of the entire distance = 3240 ÷ 2 = 1620 m

Distance that Billy ran in the first 30 min
= 3 x 1620
= 4860 m

Billy's average speed
= 4860 ÷ 30
= 162 m/min

Cody's average speed
= 162 + 108
= 270 m/min

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

¹₁₁ of the entire distance = 1620 m
⁶₁₁ of the entire distance = 6 x 1620 = 9720 m

Duration that Cody would take to complete
= 9720 ÷ 270
= 36 min

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

⁸₁₁ of the entire distance = 8 x 1620 = 12960 m  

Speed that Billy needs to take to complete distance at the same time as Cody
= 12960 ÷ 36
= 360 m/min

Increase in Billy's average speed
= 360 - 162
= 198 m/min

Percentage increase in Billy's average speed
= ¹⁹⁸₁₆₂ x 100%
≈ 122%

Answer(s): 122%