After 35 minutes into a race, Jenson has run ⁷₁₃ of the route while Ian has covered only ⁴₁₃ of the distance. Jenson runs at the same average speed throughout the race and Ian’s average speed is 102 m/min slower than Jenson’s. If Ian 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 Ian in first 35 min
= 35 x 102
= 3570 m

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

³₁₃ of the entire distance = 3570 m
¹₁₃ of the entire distance = 3570 ÷ 3 = 1190 m

Distance that Ian ran in the first 35 min
= 4 x 1190
= 4760 m

Ian's average speed
= 4760 ÷ 35
= 136 m/min

Jenson's average speed
= 136 + 102
= 238 m/min

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

¹₁₃ of the entire distance = 1190 m
⁶₁₃ of the entire distance = 6 x 1190 = 7140 m

Duration that Jenson would take to complete
= 7140 ÷ 238
= 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 1190 = 10710 m  

Speed that Ian needs to take to complete distance at the same time as Jenson
= 10710 ÷ 30
= 357 m/min

Increase in Ian's average speed
= 357 - 136
= 221 m/min

Percentage increase in Ian's average speed
= ²²¹₁₃₆ x 100%
≈ 163%

Answer(s): 163%