After 40 minutes into a race, Albert has run ⁸₁₁ of the route while Peter has covered only ²₁₁ of the distance. Albert runs at the same average speed throughout the race and Peter’s average speed is 66 m/min slower than Albert’s. If Peter wants to finish the race at the same time as Albert, 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 Albert ran more than Peter in first 40 min
= 40 x 66
= 2640 m

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

⁶₁₁ of the entire distance = 2640 m
¹₁₁ of the entire distance = 2640 ÷ 6 = 440 m

Distance that Peter ran in the first 40 min
= 2 x 440
= 880 m

Peter's average speed
= 880 ÷ 40
= 22 m/min

Albert's average speed
= 22 + 66
= 88 m/min

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

¹₁₁ of the entire distance = 440 m
³₁₁ of the entire distance = 3 x 440 = 1320 m

Duration that Albert would take to complete
= 1320 ÷ 88
= 15 min

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

⁹₁₁ of the entire distance = 9 x 440 = 3960 m  

Speed that Peter needs to take to complete distance at the same time as Albert
= 3960 ÷ 15
= 264 m/min

Increase in Peter's average speed
= 264 - 22
= 242 m/min

Percentage increase in Peter's average speed
= ²⁴²₂₂ x 100%
≈ 1100%

Answer(s): 1100%