After 40 minutes into a race, Tim has run ⁸₁₁ of the route while Owen has covered only ²₁₁ of the distance. Tim runs at the same average speed throughout the race and Owen’s average speed is 72 m/min slower than Tim’s. If Owen 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 Owen in first 40 min
= 40 x 72
= 2880 m

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

⁶₁₁ of the entire distance = 2880 m
¹₁₁ of the entire distance = 2880 ÷ 6 = 480 m

Distance that Owen ran in the first 40 min
= 2 x 480
= 960 m

Owen's average speed
= 960 ÷ 40
= 24 m/min

Tim's average speed
= 24 + 72
= 96 m/min

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

¹₁₁ of the entire distance = 480 m
³₁₁ of the entire distance = 3 x 480 = 1440 m

Duration that Tim would take to complete
= 1440 ÷ 96
= 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 480 = 4320 m  

Speed that Owen needs to take to complete distance at the same time as Tim
= 4320 ÷ 15
= 288 m/min

Increase in Owen's average speed
= 288 - 24
= 264 m/min

Percentage increase in Owen's average speed
= ²⁶⁴₂₄ x 100%
≈ 1100%

Answer(s): 1100%