After 35 minutes into a race, Tim has run ⁷₁₃ of the route while Seth has covered only ⁴₁₃ of the distance. Tim runs at the same average speed throughout the race and Seth’s average speed is 108 m/min slower than Tim’s. If Seth wants to finish the race at the same time as Tim, 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 Tim ran more than Seth in first 35 min
= 35 x 108
= 3780 m

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

³₁₃ of the entire distance = 3780 m
¹₁₃ of the entire distance = 3780 ÷ 3 = 1260 m

Distance that Seth ran in the first 35 min
= 4 x 1260
= 5040 m

Seth's average speed
= 5040 ÷ 35
= 144 m/min

Tim's average speed
= 144 + 108
= 252 m/min

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

¹₁₃ of the entire distance = 1260 m
⁶₁₃ of the entire distance = 6 x 1260 = 7560 m

Duration that Tim would take to complete
= 7560 ÷ 252
= 30 min

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

⁹₁₃ of the entire distance = 9 x 1260 = 11340 m  

Speed that Seth needs to take to complete distance at the same time as Tim
= 11340 ÷ 30
= 378 m/min

Increase in Seth's average speed
= 378 - 144
= 234 m/min

Percentage increase in Seth's average speed
= ²³⁴₁₄₄ x 100%
≈ 163%

Answer(s): 163%