After 30 minutes into a race, George has run ⁶₁₃ of the route while Vincent has covered only ⁴₁₃ of the distance. George runs at the same average speed throughout the race and Vincent’s average speed is 112 m/min slower than George’s. If Vincent wants to finish the race at the same time as George, 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 George ran more than Vincent in first 30 min
= 30 x 112
= 3360 m

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

²₁₃ of the entire distance = 3360 m
¹₁₃ of the entire distance = 3360 ÷ 2 = 1680 m

Distance that Vincent ran in the first 30 min
= 4 x 1680
= 6720 m

Vincent's average speed
= 6720 ÷ 30
= 224 m/min

George's average speed
= 224 + 112
= 336 m/min

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

¹₁₃ of the entire distance = 1680 m
⁷₁₃ of the entire distance = 7 x 1680 = 11760 m

Duration that George would take to complete
= 11760 ÷ 336
= 35 min

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

⁹₁₃ of the entire distance = 9 x 1680 = 15120 m  

Speed that Vincent needs to take to complete distance at the same time as George
= 15120 ÷ 35
= 432 m/min

Increase in Vincent's average speed
= 432 - 224
= 208 m/min

Percentage increase in Vincent's average speed
= ²⁰⁸₂₂₄ x 100%
≈ 93%

Answer(s): 93%