After 35 minutes into a race, Tommy has run ⁷₁₃ of the route while Julian has covered only ⁴₁₃ of the distance. Tommy runs at the same average speed throughout the race and Julian’s average speed is 36 m/min slower than Tommy’s. If Julian wants to finish the race at the same time as Tommy, 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 Tommy ran more than Julian in first 35 min
= 35 x 36
= 1260 m

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

³₁₃ of the entire distance = 1260 m
¹₁₃ of the entire distance = 1260 ÷ 3 = 420 m

Distance that Julian ran in the first 35 min
= 4 x 420
= 1680 m

Julian's average speed
= 1680 ÷ 35
= 48 m/min

Tommy's average speed
= 48 + 36
= 84 m/min

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

¹₁₃ of the entire distance = 420 m
⁶₁₃ of the entire distance = 6 x 420 = 2520 m

Duration that Tommy would take to complete
= 2520 ÷ 84
= 30 min

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

⁹₁₃ of the entire distance = 9 x 420 = 3780 m  

Speed that Julian needs to take to complete distance at the same time as Tommy
= 3780 ÷ 30
= 126 m/min

Increase in Julian's average speed
= 126 - 48
= 78 m/min

Percentage increase in Julian's average speed
= ⁷⁸₄₈ x 100%
≈ 163%

Answer(s): 163%