After 40 minutes into a race, Tim has run ⁸₁₁ of the route while Albert has covered only ²₁₁ of the distance. Tim runs at the same average speed throughout the race and Albert’s average speed is 99 m/min slower than Tim’s. If Albert wants to finish the race at the same time as Tim, 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 Tim ran more than Albert in first 40 min
= 40 x 99
= 3960 m

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

⁶₁₁ of the entire distance = 3960 m
¹₁₁ of the entire distance = 3960 ÷ 6 = 660 m

Distance that Albert ran in the first 40 min
= 2 x 660
= 1320 m

Albert's average speed
= 1320 ÷ 40
= 33 m/min

Tim's average speed
= 33 + 99
= 132 m/min

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

¹₁₁ of the entire distance = 660 m
³₁₁ of the entire distance = 3 x 660 = 1980 m

Duration that Tim would take to complete
= 1980 ÷ 132
= 15 min

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

⁹₁₁ of the entire distance = 9 x 660 = 5940 m  

Speed that Albert needs to take to complete distance at the same time as Tim
= 5940 ÷ 15
= 396 m/min

Increase in Albert's average speed
= 396 - 33
= 363 m/min

Percentage increase in Albert's average speed
= ³⁶³₃₃ x 100%
≈ 1100%

Answer(s): 1100%