After 30 minutes into a race, Fabian has run ⁵₁₁ of the route while Daniel has covered only ³₁₁ of the distance. Fabian runs at the same average speed throughout the race and Daniel’s average speed is 66 m/min slower than Fabian’s. If Daniel 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 Daniel in first 30 min
= 30 x 66
= 1980 m

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

²₁₁ of the entire distance = 1980 m
¹₁₁ of the entire distance = 1980 ÷ 2 = 990 m

Distance that Daniel ran in the first 30 min
= 3 x 990
= 2970 m

Daniel's average speed
= 2970 ÷ 30
= 99 m/min

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

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

¹₁₁ of the entire distance = 990 m
⁶₁₁ of the entire distance = 6 x 990 = 5940 m

Duration that Fabian would take to complete
= 5940 ÷ 165
= 36 min

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

⁸₁₁ of the entire distance = 8 x 990 = 7920 m  

Speed that Daniel needs to take to complete distance at the same time as Fabian
= 7920 ÷ 36
= 220 m/min

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

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

Answer(s): 122%