After 35 minutes into a race, Warren has run ⁵₁₁ of the route while John has covered only ³₁₁ of the distance. Warren runs at the same average speed throughout the race and John’s average speed is 120 m/min slower than Warren’s. If John wants to finish the race at the same time as Warren, 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 Warren ran more than John in first 35 min
= 35 x 120
= 4200 m

Fraction of the entire distance that was covered by Warren more than John in the first 35 min
= ⁵₁₁ - ³₁₁
= ²₁₁

²₁₁ of the entire distance = 4200 m
¹₁₁ of the entire distance = 4200 ÷ 2 = 2100 m

Distance that John ran in the first 35 min
= 3 x 2100
= 6300 m

John's average speed
= 6300 ÷ 35
= 180 m/min

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

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

¹₁₁ of the entire distance = 2100 m
⁶₁₁ of the entire distance = 6 x 2100 = 12600 m

Duration that Warren would take to complete
= 12600 ÷ 300
= 42 min

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

⁸₁₁ of the entire distance = 8 x 2100 = 16800 m  

Speed that John needs to take to complete distance at the same time as Warren
= 16800 ÷ 42
= 400 m/min

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

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

Answer(s): 122%