After 30 minutes into a race, Lee has run ⁵₁₁ of the route while Charlie has covered only ³₁₁ of the distance. Lee runs at the same average speed throughout the race and Charlie’s average speed is 90 m/min slower than Lee’s. If Charlie wants to finish the race at the same time as Lee, 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 Lee ran more than Charlie in first 30 min
= 30 x 90
= 2700 m

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

²₁₁ of the entire distance = 2700 m
¹₁₁ of the entire distance = 2700 ÷ 2 = 1350 m

Distance that Charlie ran in the first 30 min
= 3 x 1350
= 4050 m

Charlie's average speed
= 4050 ÷ 30
= 135 m/min

Lee's average speed
= 135 + 90
= 225 m/min

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

¹₁₁ of the entire distance = 1350 m
⁶₁₁ of the entire distance = 6 x 1350 = 8100 m

Duration that Lee would take to complete
= 8100 ÷ 225
= 36 min

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

⁸₁₁ of the entire distance = 8 x 1350 = 10800 m  

Speed that Charlie needs to take to complete distance at the same time as Lee
= 10800 ÷ 36
= 300 m/min

Increase in Charlie's average speed
= 300 - 135
= 165 m/min

Percentage increase in Charlie's average speed
= ¹⁶⁵₁₃₅ x 100%
≈ 122%

Answer(s): 122%