After 35 minutes into a race, Wesley has run ⁷₁₃ of the route while Zeph has covered only ⁴₁₃ of the distance. Wesley runs at the same average speed throughout the race and Zeph’s average speed is 60 m/min slower than Wesley’s. If Zeph wants to finish the race at the same time as Wesley, 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 Wesley ran more than Zeph in first 35 min
= 35 x 60
= 2100 m

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

³₁₃ of the entire distance = 2100 m
¹₁₃ of the entire distance = 2100 ÷ 3 = 700 m

Distance that Zeph ran in the first 35 min
= 4 x 700
= 2800 m

Zeph's average speed
= 2800 ÷ 35
= 80 m/min

Wesley's average speed
= 80 + 60
= 140 m/min

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

¹₁₃ of the entire distance = 700 m
⁶₁₃ of the entire distance = 6 x 700 = 4200 m

Duration that Wesley would take to complete
= 4200 ÷ 140
= 30 min

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

⁹₁₃ of the entire distance = 9 x 700 = 6300 m  

Speed that Zeph needs to take to complete distance at the same time as Wesley
= 6300 ÷ 30
= 210 m/min

Increase in Zeph's average speed
= 210 - 80
= 130 m/min

Percentage increase in Zeph's average speed
= ¹³⁰₈₀ x 100%
≈ 163%

Answer(s): 163%