After 25 minutes into a race, Vaidev has run ⁵₁₁ of the route while John has covered only ²₁₁ of the distance. Vaidev runs at the same average speed throughout the race and John’s average speed is 42 m/min slower than Vaidev’s. If John wants to finish the race at the same time as Vaidev, 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 Vaidev ran more than John in first 25 min
= 25 x 42
= 1050 m

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

³₁₁ of the entire distance = 1050 m
¹₁₁ of the entire distance = 1050 ÷ 3 = 350 m

Distance that John ran in the first 25 min
= 2 x 350
= 700 m

John's average speed
= 700 ÷ 25
= 28 m/min

Vaidev's average speed
= 28 + 42
= 70 m/min

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

¹₁₁ of the entire distance = 350 m
⁶₁₁ of the entire distance = 6 x 350 = 2100 m

Duration that Vaidev would take to complete
= 2100 ÷ 70
= 30 min

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

⁹₁₁ of the entire distance = 9 x 350 = 3150 m  

Speed that John needs to take to complete distance at the same time as Vaidev
= 3150 ÷ 30
= 105 m/min

Increase in John's average speed
= 105 - 28
= 77 m/min

Percentage increase in John's average speed
= ⁷⁷₂₈ x 100%
≈ 275%

Answer(s): 275%