After 30 minutes into a race, Ryan has run ⁶₁₃ of the route while Fabian has covered only ⁴₁₃ of the distance. Ryan runs at the same average speed throughout the race and Fabian’s average speed is 91 m/min slower than Ryan’s. If Fabian wants to finish the race at the same time as Ryan, 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 Ryan ran more than Fabian in first 30 min
= 30 x 91
= 2730 m

Fraction of the entire distance that was covered by Ryan more than Fabian in the first 30 min
= ⁶₁₃ - ⁴₁₃
= ²₁₃

²₁₃ of the entire distance = 2730 m
¹₁₃ of the entire distance = 2730 ÷ 2 = 1365 m

Distance that Fabian ran in the first 30 min
= 4 x 1365
= 5460 m

Fabian's average speed
= 5460 ÷ 30
= 182 m/min

Ryan's average speed
= 182 + 91
= 273 m/min

Fraction of the journey that Ryan needed to run to complete the race
= 1 - ⁶₁₃
= ⁷₁₃

¹₁₃ of the entire distance = 1365 m
⁷₁₃ of the entire distance = 7 x 1365 = 9555 m

Duration that Ryan would take to complete
= 9555 ÷ 273
= 35 min

Fraction of the journey that Ryan needed to run to complete the race
= 1 - ⁴₁₃
= ⁹₁₃

⁹₁₃ of the entire distance = 9 x 1365 = 12285 m  

Speed that Fabian needs to take to complete distance at the same time as Ryan
= 12285 ÷ 35
= 351 m/min

Increase in Fabian's average speed
= 351 - 182
= 169 m/min

Percentage increase in Fabian's average speed
= ¹⁶⁹₁₈₂ x 100%
≈ 93%

Answer(s): 93%