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

Fraction of the entire distance that was covered by Billy more than Ryan 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 Ryan ran in the first 30 min
= 2 x 900
= 1800 m

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

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

Fraction of the journey that Billy 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 Billy would take to complete
= 5400 ÷ 150
= 36 min

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

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

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

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

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

Answer(s): 275%