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

Fraction of the entire distance that was covered by Cole more than Oliver 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 Oliver ran in the first 30 min
= 4 x 1785
= 7140 m

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

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

Fraction of the journey that Cole 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 Cole would take to complete
= 12495 ÷ 357
= 35 min

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

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

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

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

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

Answer(s): 93%