After 25 minutes into a race, Caden has run ⁵₁₁ of the route while Harry has covered only ³₁₁ of the distance. Caden runs at the same average speed throughout the race and Harry’s average speed is 66 m/min slower than Caden’s. If Harry 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 Harry in first 25 min
= 25 x 66
= 1650 m

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

²₁₁ of the entire distance = 1650 m
¹₁₁ of the entire distance = 1650 ÷ 2 = 825 m

Distance that Harry ran in the first 25 min
= 3 x 825
= 2475 m

Harry's average speed
= 2475 ÷ 25
= 99 m/min

Caden's average speed
= 99 + 66
= 165 m/min

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

¹₁₁ of the entire distance = 825 m
⁶₁₁ of the entire distance = 6 x 825 = 4950 m

Duration that Caden would take to complete
= 4950 ÷ 165
= 30 min

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

⁸₁₁ of the entire distance = 8 x 825 = 6600 m  

Speed that Harry needs to take to complete distance at the same time as Caden
= 6600 ÷ 30
= 220 m/min

Increase in Harry's average speed
= 220 - 99
= 121 m/min

Percentage increase in Harry's average speed
= ¹²¹₉₉ x 100%
≈ 122%

Answer(s): 122%