After 30 minutes into a race, Simon has run ⁵₁₁ of the route while Lee has covered only ²₁₁ of the distance. Simon runs at the same average speed throughout the race and Lee’s average speed is 66 m/min slower than Simon’s. If Lee wants to finish the race at the same time as Simon, 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 Simon ran more than Lee in first 30 min
= 30 x 66
= 1980 m

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

³₁₁ of the entire distance = 1980 m
¹₁₁ of the entire distance = 1980 ÷ 3 = 660 m

Distance that Lee ran in the first 30 min
= 2 x 660
= 1320 m

Lee's average speed
= 1320 ÷ 30
= 44 m/min

Simon's average speed
= 44 + 66
= 110 m/min

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

¹₁₁ of the entire distance = 660 m
⁶₁₁ of the entire distance = 6 x 660 = 3960 m

Duration that Simon would take to complete
= 3960 ÷ 110
= 36 min

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

⁹₁₁ of the entire distance = 9 x 660 = 5940 m  

Speed that Lee needs to take to complete distance at the same time as Simon
= 5940 ÷ 36
= 165 m/min

Increase in Lee's average speed
= 165 - 44
= 121 m/min

Percentage increase in Lee's average speed
= ¹²¹₄₄ x 100%
≈ 275%

Answer(s): 275%