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

Fraction of the entire distance that was covered by Zane more than Bryan 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 Bryan ran in the first 30 min
= 4 x 1365
= 5460 m

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

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

Fraction of the journey that Zane 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 Zane would take to complete
= 9555 ÷ 273
= 35 min

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

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

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

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

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

Answer(s): 93%