After 30 minutes into a race, Rael has run ⁶₁₃ of the route while George has covered only ⁴₁₃ of the distance. Rael runs at the same average speed throughout the race and George’s average speed is 70 m/min slower than Rael’s. If George wants to finish the race at the same time as Rael, 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 Rael ran more than George in first 30 min
= 30 x 70
= 2100 m

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

²₁₃ of the entire distance = 2100 m
¹₁₃ of the entire distance = 2100 ÷ 2 = 1050 m

Distance that George ran in the first 30 min
= 4 x 1050
= 4200 m

George's average speed
= 4200 ÷ 30
= 140 m/min

Rael's average speed
= 140 + 70
= 210 m/min

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

¹₁₃ of the entire distance = 1050 m
⁷₁₃ of the entire distance = 7 x 1050 = 7350 m

Duration that Rael would take to complete
= 7350 ÷ 210
= 35 min

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

⁹₁₃ of the entire distance = 9 x 1050 = 9450 m  

Speed that George needs to take to complete distance at the same time as Rael
= 9450 ÷ 35
= 270 m/min

Increase in George's average speed
= 270 - 140
= 130 m/min

Percentage increase in George's average speed
= ¹³⁰₁₄₀ x 100%
≈ 93%

Answer(s): 93%