After 35 minutes into a race, Vaidev has run ⁷₁₃ of the route while Archie has covered only ⁴₁₃ of the distance. Vaidev runs at the same average speed throughout the race and Archie’s average speed is 48 m/min slower than Vaidev’s. If Archie 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 Archie in first 35 min
= 35 x 48
= 1680 m

Fraction of the entire distance that was covered by Vaidev more than Archie in the first 35 min
= ⁷₁₃ - ⁴₁₃
= ³₁₃

³₁₃ of the entire distance = 1680 m
¹₁₃ of the entire distance = 1680 ÷ 3 = 560 m

Distance that Archie ran in the first 35 min
= 4 x 560
= 2240 m

Archie's average speed
= 2240 ÷ 35
= 64 m/min

Vaidev's average speed
= 64 + 48
= 112 m/min

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

¹₁₃ of the entire distance = 560 m
⁶₁₃ of the entire distance = 6 x 560 = 3360 m

Duration that Vaidev would take to complete
= 3360 ÷ 112
= 30 min

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

⁹₁₃ of the entire distance = 9 x 560 = 5040 m  

Speed that Archie needs to take to complete distance at the same time as Vaidev
= 5040 ÷ 30
= 168 m/min

Increase in Archie's average speed
= 168 - 64
= 104 m/min

Percentage increase in Archie's average speed
= ¹⁰⁴₆₄ x 100%
≈ 163%

Answer(s): 163%