After 30 minutes into a race, Oscar has run ⁵₁₁ of the route while Riordan has covered only ²₁₁ of the distance. Oscar runs at the same average speed throughout the race and Riordan’s average speed is 96 m/min slower than Oscar’s. If Riordan wants to finish the race at the same time as Oscar, 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 Oscar ran more than Riordan in first 30 min
= 30 x 96
= 2880 m

Fraction of the entire distance that was covered by Oscar more than Riordan in the first 30 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 2880 m
¹₁₁ of the entire distance = 2880 ÷ 3 = 960 m

Distance that Riordan ran in the first 30 min
= 2 x 960
= 1920 m

Riordan's average speed
= 1920 ÷ 30
= 64 m/min

Oscar's average speed
= 64 + 96
= 160 m/min

Fraction of the journey that Oscar needed to run to complete the race
= 1 - ⁵₁₁
= ⁶₁₁

¹₁₁ of the entire distance = 960 m
⁶₁₁ of the entire distance = 6 x 960 = 5760 m

Duration that Oscar would take to complete
= 5760 ÷ 160
= 36 min

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

⁹₁₁ of the entire distance = 9 x 960 = 8640 m  

Speed that Riordan needs to take to complete distance at the same time as Oscar
= 8640 ÷ 36
= 240 m/min

Increase in Riordan's average speed
= 240 - 64
= 176 m/min

Percentage increase in Riordan's average speed
= ¹⁷⁶₆₄ x 100%
≈ 275%

Answer(s): 275%