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

Fraction of the entire distance that was covered by Owen more than Jeremy 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 Jeremy ran in the first 35 min
= 4 x 420
= 1680 m

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

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

Fraction of the journey that Owen 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 Owen would take to complete
= 2520 ÷ 84
= 30 min

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

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

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

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

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

Answer(s): 163%