After 30 minutes into a race, Fred has run ⁶₁₃ of the route while Vaidev has covered only ⁴₁₃ of the distance. Fred runs at the same average speed throughout the race and Vaidev’s average speed is 91 m/min slower than Fred’s. If Vaidev wants to finish the race at the same time as Fred, 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 Fred ran more than Vaidev in first 30 min
= 30 x 91
= 2730 m

Fraction of the entire distance that was covered by Fred more than Vaidev in the first 30 min
= ⁶₁₃ - ⁴₁₃
= ²₁₃

²₁₃ of the entire distance = 2730 m
¹₁₃ of the entire distance = 2730 ÷ 2 = 1365 m

Distance that Vaidev ran in the first 30 min
= 4 x 1365
= 5460 m

Vaidev's average speed
= 5460 ÷ 30
= 182 m/min

Fred's average speed
= 182 + 91
= 273 m/min

Fraction of the journey that Fred needed to run to complete the race
= 1 - ⁶₁₃
= ⁷₁₃

¹₁₃ of the entire distance = 1365 m
⁷₁₃ of the entire distance = 7 x 1365 = 9555 m

Duration that Fred would take to complete
= 9555 ÷ 273
= 35 min

Fraction of the journey that Fred needed to run to complete the race
= 1 - ⁴₁₃
= ⁹₁₃

⁹₁₃ of the entire distance = 9 x 1365 = 12285 m  

Speed that Vaidev needs to take to complete distance at the same time as Fred
= 12285 ÷ 35
= 351 m/min

Increase in Vaidev's average speed
= 351 - 182
= 169 m/min

Percentage increase in Vaidev's average speed
= ¹⁶⁹₁₈₂ x 100%
≈ 93%

Answer(s): 93%