After 40 minutes into a race, Will has run ⁸₁₁ of the route while Michael has covered only ²₁₁ of the distance. Will runs at the same average speed throughout the race and Michael’s average speed is 84 m/min slower than Will’s. If Michael wants to finish the race at the same time as Will, 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 Will ran more than Michael in first 40 min
= 40 x 84
= 3360 m

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

⁶₁₁ of the entire distance = 3360 m
¹₁₁ of the entire distance = 3360 ÷ 6 = 560 m

Distance that Michael ran in the first 40 min
= 2 x 560
= 1120 m

Michael's average speed
= 1120 ÷ 40
= 28 m/min

Will's average speed
= 28 + 84
= 112 m/min

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

¹₁₁ of the entire distance = 560 m
³₁₁ of the entire distance = 3 x 560 = 1680 m

Duration that Will would take to complete
= 1680 ÷ 112
= 15 min

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

⁹₁₁ of the entire distance = 9 x 560 = 5040 m  

Speed that Michael needs to take to complete distance at the same time as Will
= 5040 ÷ 15
= 336 m/min

Increase in Michael's average speed
= 336 - 28
= 308 m/min

Percentage increase in Michael's average speed
= ³⁰⁸₂₈ x 100%
≈ 1100%

Answer(s): 1100%