After 30 minutes into a race, Vaidev has run ⁵₁₁ of the route while Peter has covered only ²₁₁ of the distance. Vaidev runs at the same average speed throughout the race and Peter’s average speed is 90 m/min slower than Vaidev’s. If Peter 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 Peter in first 30 min
= 30 x 90
= 2700 m

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

³₁₁ of the entire distance = 2700 m
¹₁₁ of the entire distance = 2700 ÷ 3 = 900 m

Distance that Peter ran in the first 30 min
= 2 x 900
= 1800 m

Peter's average speed
= 1800 ÷ 30
= 60 m/min

Vaidev's average speed
= 60 + 90
= 150 m/min

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

¹₁₁ of the entire distance = 900 m
⁶₁₁ of the entire distance = 6 x 900 = 5400 m

Duration that Vaidev would take to complete
= 5400 ÷ 150
= 36 min

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

⁹₁₁ of the entire distance = 9 x 900 = 8100 m  

Speed that Peter needs to take to complete distance at the same time as Vaidev
= 8100 ÷ 36
= 225 m/min

Increase in Peter's average speed
= 225 - 60
= 165 m/min

Percentage increase in Peter's average speed
= ¹⁶⁵₆₀ x 100%
≈ 275%

Answer(s): 275%