After 25 minutes into a race, Gabriel has run ⁵₁₁ of the route while Cole has covered only ³₁₁ of the distance. Gabriel runs at the same average speed throughout the race and Cole’s average speed is 120 m/min slower than Gabriel’s. If Cole wants to finish the race at the same time as Gabriel, 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 Gabriel ran more than Cole in first 25 min
= 25 x 120
= 3000 m

Fraction of the entire distance that was covered by Gabriel more than Cole in the first 25 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 3000 m
¹₁₁ of the entire distance = 3000 ÷ 2 = 1500 m

Distance that Cole ran in the first 25 min
= 3 x 1500
= 4500 m

Cole's average speed
= 4500 ÷ 25
= 180 m/min

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

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

¹₁₁ of the entire distance = 1500 m
⁶₁₁ of the entire distance = 6 x 1500 = 9000 m

Duration that Gabriel would take to complete
= 9000 ÷ 300
= 30 min

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

⁸₁₁ of the entire distance = 8 x 1500 = 12000 m  

Speed that Cole needs to take to complete distance at the same time as Gabriel
= 12000 ÷ 30
= 400 m/min

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

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

Answer(s): 122%