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

Fraction of the entire distance that was covered by Oliver more than Carl 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 Carl ran in the first 30 min
= 4 x 1050
= 4200 m

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

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

Fraction of the journey that Oliver 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 Oliver would take to complete
= 7350 ÷ 210
= 35 min

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

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

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

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

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

Answer(s): 93%