After 30 minutes into a race, Ben has run ⁵₁₁ of the route while Flynn has covered only ²₁₁ of the distance. Ben runs at the same average speed throughout the race and Flynn’s average speed is 90 m/min slower than Ben’s. If Flynn wants to finish the race at the same time as Ben, 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 Ben ran more than Flynn in first 30 min
= 30 x 90
= 2700 m

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

³₁₁ of the entire distance = 2700 m
¹₁₁ of the entire distance = 2700 ÷ 3 = 900 m

Distance that Flynn ran in the first 30 min
= 2 x 900
= 1800 m

Flynn's average speed
= 1800 ÷ 30
= 60 m/min

Ben's average speed
= 60 + 90
= 150 m/min

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

¹₁₁ of the entire distance = 900 m
⁶₁₁ of the entire distance = 6 x 900 = 5400 m

Duration that Ben would take to complete
= 5400 ÷ 150
= 36 min

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

⁹₁₁ of the entire distance = 9 x 900 = 8100 m  

Speed that Flynn needs to take to complete distance at the same time as Ben
= 8100 ÷ 36
= 225 m/min

Increase in Flynn's average speed
= 225 - 60
= 165 m/min

Percentage increase in Flynn's average speed
= ¹⁶⁵₆₀ x 100%
≈ 275%

Answer(s): 275%