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

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

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

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

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

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

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

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

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

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

Answer(s): 93%