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

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

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

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

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

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

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

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

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

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

Answer(s): 93%