After 35 minutes into a race, Jeremy has run ⁷₁₃ of the route while Ahmad has covered only ⁴₁₃ of the distance. Jeremy runs at the same average speed throughout the race and Ahmad’s average speed is 120 m/min slower than Jeremy’s. If Ahmad wants to finish the race at the same time as Jeremy, 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 Jeremy ran more than Ahmad in first 35 min
= 35 x 120
= 4200 m

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

³₁₃ of the entire distance = 4200 m
¹₁₃ of the entire distance = 4200 ÷ 3 = 1400 m

Distance that Ahmad ran in the first 35 min
= 4 x 1400
= 5600 m

Ahmad's average speed
= 5600 ÷ 35
= 160 m/min

Jeremy's average speed
= 160 + 120
= 280 m/min

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

¹₁₃ of the entire distance = 1400 m
⁶₁₃ of the entire distance = 6 x 1400 = 8400 m

Duration that Jeremy would take to complete
= 8400 ÷ 280
= 30 min

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

⁹₁₃ of the entire distance = 9 x 1400 = 12600 m  

Speed that Ahmad needs to take to complete distance at the same time as Jeremy
= 12600 ÷ 30
= 420 m/min

Increase in Ahmad's average speed
= 420 - 160
= 260 m/min

Percentage increase in Ahmad's average speed
= ²⁶⁰₁₆₀ x 100%
≈ 163%

Answer(s): 163%