After 30 minutes into a race, Reggie has run ⁶₁₃ of the route while Justin has covered only ⁴₁₃ of the distance. Reggie runs at the same average speed throughout the race and Justin’s average speed is 119 m/min slower than Reggie’s. If Justin wants to finish the race at the same time as Reggie, 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 Reggie ran more than Justin in first 30 min
= 30 x 119
= 3570 m

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

²₁₃ of the entire distance = 3570 m
¹₁₃ of the entire distance = 3570 ÷ 2 = 1785 m

Distance that Justin ran in the first 30 min
= 4 x 1785
= 7140 m

Justin's average speed
= 7140 ÷ 30
= 238 m/min

Reggie's average speed
= 238 + 119
= 357 m/min

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

¹₁₃ of the entire distance = 1785 m
⁷₁₃ of the entire distance = 7 x 1785 = 12495 m

Duration that Reggie would take to complete
= 12495 ÷ 357
= 35 min

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

⁹₁₃ of the entire distance = 9 x 1785 = 16065 m  

Speed that Justin needs to take to complete distance at the same time as Reggie
= 16065 ÷ 35
= 459 m/min

Increase in Justin's average speed
= 459 - 238
= 221 m/min

Percentage increase in Justin's average speed
= ²²¹₂₃₈ x 100%
≈ 93%

Answer(s): 93%