After 20 minutes into a race, Andy has run ⁵₁₁ of the route while Jeremy has covered only ²₁₁ of the distance. Andy runs at the same average speed throughout the race and Jeremy’s average speed is 48 m/min slower than Andy’s. If Jeremy wants to finish the race at the same time as Andy, 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 Andy ran more than Jeremy in first 20 min
= 20 x 48
= 960 m

Fraction of the entire distance that was covered by Andy more than Jeremy in the first 20 min
= ⁵₁₁ - ²₁₁
= ³₁₁

³₁₁ of the entire distance = 960 m
¹₁₁ of the entire distance = 960 ÷ 3 = 320 m

Distance that Jeremy ran in the first 20 min
= 2 x 320
= 640 m

Jeremy's average speed
= 640 ÷ 20
= 32 m/min

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

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

¹₁₁ of the entire distance = 320 m
⁶₁₁ of the entire distance = 6 x 320 = 1920 m

Duration that Andy would take to complete
= 1920 ÷ 80
= 24 min

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

⁹₁₁ of the entire distance = 9 x 320 = 2880 m  

Speed that Jeremy needs to take to complete distance at the same time as Andy
= 2880 ÷ 24
= 120 m/min

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

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

Answer(s): 275%