After 40 minutes into a race, Dylan has run ⁸₁₁ of the route while Lee has covered only ²₁₁ of the distance. Dylan runs at the same average speed throughout the race and Lee’s average speed is 93 m/min slower than Dylan’s. If Lee wants to finish the race at the same time as Dylan, 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 Dylan ran more than Lee in first 40 min
= 40 x 93
= 3720 m

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

⁶₁₁ of the entire distance = 3720 m
¹₁₁ of the entire distance = 3720 ÷ 6 = 620 m

Distance that Lee ran in the first 40 min
= 2 x 620
= 1240 m

Lee's average speed
= 1240 ÷ 40
= 31 m/min

Dylan's average speed
= 31 + 93
= 124 m/min

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

¹₁₁ of the entire distance = 620 m
³₁₁ of the entire distance = 3 x 620 = 1860 m

Duration that Dylan would take to complete
= 1860 ÷ 124
= 15 min

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

⁹₁₁ of the entire distance = 9 x 620 = 5580 m  

Speed that Lee needs to take to complete distance at the same time as Dylan
= 5580 ÷ 15
= 372 m/min

Increase in Lee's average speed
= 372 - 31
= 341 m/min

Percentage increase in Lee's average speed
= ³⁴¹₃₁ x 100%
≈ 1100%

Answer(s): 1100%