After 20 minutes into a race, Andy has run ⁵₁₁ of the route while Billy has covered only ³₁₁ of the distance. Andy runs at the same average speed throughout the race and Billy’s average speed is 120 m/min slower than Andy’s. If Billy 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 Billy in first 20 min
= 20 x 120
= 2400 m

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

²₁₁ of the entire distance = 2400 m
¹₁₁ of the entire distance = 2400 ÷ 2 = 1200 m

Distance that Billy ran in the first 20 min
= 3 x 1200
= 3600 m

Billy's average speed
= 3600 ÷ 20
= 180 m/min

Andy's average speed
= 180 + 120
= 300 m/min

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

¹₁₁ of the entire distance = 1200 m
⁶₁₁ of the entire distance = 6 x 1200 = 7200 m

Duration that Andy would take to complete
= 7200 ÷ 300
= 24 min

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

⁸₁₁ of the entire distance = 8 x 1200 = 9600 m  

Speed that Billy needs to take to complete distance at the same time as Andy
= 9600 ÷ 24
= 400 m/min

Increase in Billy's average speed
= 400 - 180
= 220 m/min

Percentage increase in Billy's average speed
= ²²⁰₁₈₀ x 100%
≈ 122%

Answer(s): 122%