After 40 minutes into a race, Ahmad has run ⁸₁₁ of the route while Justin has covered only ²₁₁ of the distance. Ahmad runs at the same average speed throughout the race and Justin’s average speed is 45 m/min slower than Ahmad’s. If Justin wants to finish the race at the same time as Ahmad, 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 Ahmad ran more than Justin in first 40 min
= 40 x 45
= 1800 m

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

⁶₁₁ of the entire distance = 1800 m
¹₁₁ of the entire distance = 1800 ÷ 6 = 300 m

Distance that Justin ran in the first 40 min
= 2 x 300
= 600 m

Justin's average speed
= 600 ÷ 40
= 15 m/min

Ahmad's average speed
= 15 + 45
= 60 m/min

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

¹₁₁ of the entire distance = 300 m
³₁₁ of the entire distance = 3 x 300 = 900 m

Duration that Ahmad would take to complete
= 900 ÷ 60
= 15 min

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

⁹₁₁ of the entire distance = 9 x 300 = 2700 m  

Speed that Justin needs to take to complete distance at the same time as Ahmad
= 2700 ÷ 15
= 180 m/min

Increase in Justin's average speed
= 180 - 15
= 165 m/min

Percentage increase in Justin's average speed
= ¹⁶⁵₁₅ x 100%
≈ 1100%

Answer(s): 1100%