After 40 minutes into a race, Howard has run ⁸₁₁ of the route while Riordan has covered only ²₁₁ of the distance. Howard runs at the same average speed throughout the race and Riordan’s average speed is 30 m/min slower than Howard’s. If Riordan wants to finish the race at the same time as Howard, 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 Howard ran more than Riordan in first 40 min
= 40 x 30
= 1200 m

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

⁶₁₁ of the entire distance = 1200 m
¹₁₁ of the entire distance = 1200 ÷ 6 = 200 m

Distance that Riordan ran in the first 40 min
= 2 x 200
= 400 m

Riordan's average speed
= 400 ÷ 40
= 10 m/min

Howard's average speed
= 10 + 30
= 40 m/min

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

¹₁₁ of the entire distance = 200 m
³₁₁ of the entire distance = 3 x 200 = 600 m

Duration that Howard would take to complete
= 600 ÷ 40
= 15 min

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

⁹₁₁ of the entire distance = 9 x 200 = 1800 m  

Speed that Riordan needs to take to complete distance at the same time as Howard
= 1800 ÷ 15
= 120 m/min

Increase in Riordan's average speed
= 120 - 10
= 110 m/min

Percentage increase in Riordan's average speed
= ¹¹⁰₁₀ x 100%
≈ 1100%

Answer(s): 1100%