After 40 minutes into a race, Bobby has run ⁸₁₁ of the route while Jeremy has covered only ²₁₁ of the distance. Bobby runs at the same average speed throughout the race and Jeremy’s average speed is 45 m/min slower than Bobby’s. If Jeremy wants to finish the race at the same time as Bobby, 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 Bobby ran more than Jeremy in first 40 min
= 40 x 45
= 1800 m

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

⁶₁₁ of the entire distance = 1800 m
¹₁₁ of the entire distance = 1800 ÷ 6 = 300 m

Distance that Jeremy ran in the first 40 min
= 2 x 300
= 600 m

Jeremy's average speed
= 600 ÷ 40
= 15 m/min

Bobby's average speed
= 15 + 45
= 60 m/min

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

¹₁₁ of the entire distance = 300 m
³₁₁ of the entire distance = 3 x 300 = 900 m

Duration that Bobby would take to complete
= 900 ÷ 60
= 15 min

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

⁹₁₁ of the entire distance = 9 x 300 = 2700 m  

Speed that Jeremy needs to take to complete distance at the same time as Bobby
= 2700 ÷ 15
= 180 m/min

Increase in Jeremy's average speed
= 180 - 15
= 165 m/min

Percentage increase in Jeremy's average speed
= ¹⁶⁵₁₅ x 100%
≈ 1100%

Answer(s): 1100%