After 35 minutes into a race, Jenson has run ⁷₁₃ of the route while Zane has covered only ⁴₁₃ of the distance. Jenson runs at the same average speed throughout the race and Zane’s average speed is 78 m/min slower than Jenson’s. If Zane wants to finish the race at the same time as Jenson, 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 Jenson ran more than Zane in first 35 min
= 35 x 78
= 2730 m

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

³₁₃ of the entire distance = 2730 m
¹₁₃ of the entire distance = 2730 ÷ 3 = 910 m

Distance that Zane ran in the first 35 min
= 4 x 910
= 3640 m

Zane's average speed
= 3640 ÷ 35
= 104 m/min

Jenson's average speed
= 104 + 78
= 182 m/min

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

¹₁₃ of the entire distance = 910 m
⁶₁₃ of the entire distance = 6 x 910 = 5460 m

Duration that Jenson would take to complete
= 5460 ÷ 182
= 30 min

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

⁹₁₃ of the entire distance = 9 x 910 = 8190 m  

Speed that Zane needs to take to complete distance at the same time as Jenson
= 8190 ÷ 30
= 273 m/min

Increase in Zane's average speed
= 273 - 104
= 169 m/min

Percentage increase in Zane's average speed
= ¹⁶⁹₁₀₄ x 100%
≈ 163%

Answer(s): 163%