After 40 minutes into a race, Oliver has run ⁸₁₁ of the route while Luis has covered only ²₁₁ of the distance. Oliver runs at the same average speed throughout the race and Luis’s average speed is 78 m/min slower than Oliver’s. If Luis 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 Luis in first 40 min
= 40 x 78
= 3120 m

Fraction of the entire distance that was covered by Oliver more than Luis in the first 40 min
= ⁸₁₁ - ²₁₁
= ⁶₁₁

⁶₁₁ of the entire distance = 3120 m
¹₁₁ of the entire distance = 3120 ÷ 6 = 520 m

Distance that Luis ran in the first 40 min
= 2 x 520
= 1040 m

Luis's average speed
= 1040 ÷ 40
= 26 m/min

Oliver's average speed
= 26 + 78
= 104 m/min

Fraction of the journey that Oliver needed to run to complete the race
= 1 - ⁸₁₁
= ³₁₁

¹₁₁ of the entire distance = 520 m
³₁₁ of the entire distance = 3 x 520 = 1560 m

Duration that Oliver would take to complete
= 1560 ÷ 104
= 15 min

Fraction of the journey that Oliver needed to run to complete the race
= 1 - ²₁₁
= ⁹₁₁

⁹₁₁ of the entire distance = 9 x 520 = 4680 m  

Speed that Luis needs to take to complete distance at the same time as Oliver
= 4680 ÷ 15
= 312 m/min

Increase in Luis's average speed
= 312 - 26
= 286 m/min

Percentage increase in Luis's average speed
= ²⁸⁶₂₆ x 100%
≈ 1100%

Answer(s): 1100%