After 30 minutes into a race, Ken has run ⁵₁₁ of the route while Gabriel has covered only ³₁₁ of the distance. Ken runs at the same average speed throughout the race and Gabriel’s average speed is 30 m/min slower than Ken’s. If Gabriel wants to finish the race at the same time as Ken, 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 Ken ran more than Gabriel in first 30 min
= 30 x 30
= 900 m

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

²₁₁ of the entire distance = 900 m
¹₁₁ of the entire distance = 900 ÷ 2 = 450 m

Distance that Gabriel ran in the first 30 min
= 3 x 450
= 1350 m

Gabriel's average speed
= 1350 ÷ 30
= 45 m/min

Ken's average speed
= 45 + 30
= 75 m/min

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

¹₁₁ of the entire distance = 450 m
⁶₁₁ of the entire distance = 6 x 450 = 2700 m

Duration that Ken would take to complete
= 2700 ÷ 75
= 36 min

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

⁸₁₁ of the entire distance = 8 x 450 = 3600 m  

Speed that Gabriel needs to take to complete distance at the same time as Ken
= 3600 ÷ 36
= 100 m/min

Increase in Gabriel's average speed
= 100 - 45
= 55 m/min

Percentage increase in Gabriel's average speed
= ⁵⁵₄₅ x 100%
≈ 122%

Answer(s): 122%