After 35 minutes into a race, Julian has run ⁷₁₃ of the route while Xavier has covered only ⁴₁₃ of the distance. Julian runs at the same average speed throughout the race and Xavier’s average speed is 108 m/min slower than Julian’s. If Xavier wants to finish the race at the same time as Julian, 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 Julian ran more than Xavier in first 35 min
= 35 x 108
= 3780 m

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

³₁₃ of the entire distance = 3780 m
¹₁₃ of the entire distance = 3780 ÷ 3 = 1260 m

Distance that Xavier ran in the first 35 min
= 4 x 1260
= 5040 m

Xavier's average speed
= 5040 ÷ 35
= 144 m/min

Julian's average speed
= 144 + 108
= 252 m/min

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

¹₁₃ of the entire distance = 1260 m
⁶₁₃ of the entire distance = 6 x 1260 = 7560 m

Duration that Julian would take to complete
= 7560 ÷ 252
= 30 min

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

⁹₁₃ of the entire distance = 9 x 1260 = 11340 m  

Speed that Xavier needs to take to complete distance at the same time as Julian
= 11340 ÷ 30
= 378 m/min

Increase in Xavier's average speed
= 378 - 144
= 234 m/min

Percentage increase in Xavier's average speed
= ²³⁴₁₄₄ x 100%
≈ 163%

Answer(s): 163%