After 40 minutes into a race, Justin has run ⁸₁₁ of the route while Simon has covered only ²₁₁ of the distance. Justin runs at the same average speed throughout the race and Simon’s average speed is 63 m/min slower than Justin’s. If Simon wants to finish the race at the same time as Justin, 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 Justin ran more than Simon in first 40 min
= 40 x 63
= 2520 m

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

⁶₁₁ of the entire distance = 2520 m
¹₁₁ of the entire distance = 2520 ÷ 6 = 420 m

Distance that Simon ran in the first 40 min
= 2 x 420
= 840 m

Simon's average speed
= 840 ÷ 40
= 21 m/min

Justin's average speed
= 21 + 63
= 84 m/min

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

¹₁₁ of the entire distance = 420 m
³₁₁ of the entire distance = 3 x 420 = 1260 m

Duration that Justin would take to complete
= 1260 ÷ 84
= 15 min

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

⁹₁₁ of the entire distance = 9 x 420 = 3780 m  

Speed that Simon needs to take to complete distance at the same time as Justin
= 3780 ÷ 15
= 252 m/min

Increase in Simon's average speed
= 252 - 21
= 231 m/min

Percentage increase in Simon's average speed
= ²³¹₂₁ x 100%
≈ 1100%

Answer(s): 1100%