After 40 minutes into a race, Rael has run ⁸₁₁ of the route while Harry has covered only ²₁₁ of the distance. Rael runs at the same average speed throughout the race and Harry’s average speed is 117 m/min slower than Rael’s. If Harry wants to finish the race at the same time as Rael, 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 Rael ran more than Harry in first 40 min
= 40 x 117
= 4680 m

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

⁶₁₁ of the entire distance = 4680 m
¹₁₁ of the entire distance = 4680 ÷ 6 = 780 m

Distance that Harry ran in the first 40 min
= 2 x 780
= 1560 m

Harry's average speed
= 1560 ÷ 40
= 39 m/min

Rael's average speed
= 39 + 117
= 156 m/min

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

¹₁₁ of the entire distance = 780 m
³₁₁ of the entire distance = 3 x 780 = 2340 m

Duration that Rael would take to complete
= 2340 ÷ 156
= 15 min

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

⁹₁₁ of the entire distance = 9 x 780 = 7020 m  

Speed that Harry needs to take to complete distance at the same time as Rael
= 7020 ÷ 15
= 468 m/min

Increase in Harry's average speed
= 468 - 39
= 429 m/min

Percentage increase in Harry's average speed
= ⁴²⁹₃₉ x 100%
≈ 1100%

Answer(s): 1100%