After 40 minutes into a race, Bryan has run ⁵₁₁ of the route while Howard has covered only ²₁₁ of the distance. Bryan runs at the same average speed throughout the race and Howard’s average speed is 48 m/min slower than Bryan’s. If Howard wants to finish the race at the same time as Bryan, 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 Bryan ran more than Howard in first 40 min
= 40 x 48
= 1920 m

Fraction of the entire distance that was covered by Bryan more than Howard in the first 40 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 1920 m
¹₁₁ of the entire distance = 1920 ÷ 3 = 640 m

Distance that Howard ran in the first 40 min
= 2 x 640
= 1280 m

Howard's average speed
= 1280 ÷ 40
= 32 m/min

Bryan's average speed
= 32 + 48
= 80 m/min

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

¹₁₁ of the entire distance = 640 m
⁶₁₁ of the entire distance = 6 x 640 = 3840 m

Duration that Bryan would take to complete
= 3840 ÷ 80
= 48 min

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

⁹₁₁ of the entire distance = 9 x 640 = 5760 m  

Speed that Howard needs to take to complete distance at the same time as Bryan
= 5760 ÷ 48
= 120 m/min

Increase in Howard's average speed
= 120 - 32
= 88 m/min

Percentage increase in Howard's average speed
= ⁸⁸₃₂ x 100%
≈ 275%

Answer(s): 275%